The minimal model program for orders over surfaces

Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Chan, Daniel [verfasserIn] Ingalls, Colin

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2005

Schlagwörter:	Model Program Local Structure Minimal Model Algebraic Surface Minimal Model Program

Anmerkung:	© Springer-Verlag 2005

Übergeordnetes Werk:	Enthalten in: Inventiones mathematicae - Berlin : Springer, 1966, 161(2005), 2 vom: 14. Juni, Seite 427-452
Übergeordnetes Werk:	volume:161 ; year:2005 ; number:2 ; day:14 ; month:06 ; pages:427-452

Links:	Volltext

DOI / URN:	10.1007/s00222-005-0438-z

Katalog-ID:	SPR002449218

Internformat


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520			\|a Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo.
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650		4	\|a Local Structure \|7 (dpeaa)DE-He213
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650		4	\|a Algebraic Surface \|7 (dpeaa)DE-He213
650		4	\|a Minimal Model Program \|7 (dpeaa)DE-He213
700	1		\|a Ingalls, Colin \|4 aut
773	0	8	\|i Enthalten in \|t Inventiones mathematicae \|d Berlin : Springer, 1966 \|g 161(2005), 2 vom: 14. Juni, Seite 427-452 \|w (DE-627)235503525 \|w (DE-600)1398341-6 \|x 1432-1297 \|7 nnns
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912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
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912			\|a GBV_ILN_2055
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912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
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912			\|a GBV_ILN_2070
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912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
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912			\|a GBV_ILN_2111
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912			\|a GBV_ILN_2232
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912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
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912			\|a GBV_ILN_4336
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Indexfelder

author_variant	d c dc c i ci
matchkey_str	article:14321297:2005----::hmnmloepormoodr
hierarchy_sort_str	2005
publishDate	2005
allfields	10.1007/s00222-005-0438-z doi (DE-627)SPR002449218 (SPR)s00222-005-0438-z-e DE-627 ger DE-627 rakwb eng Chan, Daniel verfasserin aut The minimal model program for orders over surfaces 2005 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2005 Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213 Ingalls, Colin aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 161(2005), 2 vom: 14. Juni, Seite 427-452 (DE-627)235503525 (DE-600)1398341-6 1432-1297 nnns volume:161 year:2005 number:2 day:14 month:06 pages:427-452 https://dx.doi.org/10.1007/s00222-005-0438-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 161 2005 2 14 06 427-452
spelling	10.1007/s00222-005-0438-z doi (DE-627)SPR002449218 (SPR)s00222-005-0438-z-e DE-627 ger DE-627 rakwb eng Chan, Daniel verfasserin aut The minimal model program for orders over surfaces 2005 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2005 Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213 Ingalls, Colin aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 161(2005), 2 vom: 14. Juni, Seite 427-452 (DE-627)235503525 (DE-600)1398341-6 1432-1297 nnns volume:161 year:2005 number:2 day:14 month:06 pages:427-452 https://dx.doi.org/10.1007/s00222-005-0438-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 161 2005 2 14 06 427-452
allfields_unstemmed	10.1007/s00222-005-0438-z doi (DE-627)SPR002449218 (SPR)s00222-005-0438-z-e DE-627 ger DE-627 rakwb eng Chan, Daniel verfasserin aut The minimal model program for orders over surfaces 2005 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2005 Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213 Ingalls, Colin aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 161(2005), 2 vom: 14. Juni, Seite 427-452 (DE-627)235503525 (DE-600)1398341-6 1432-1297 nnns volume:161 year:2005 number:2 day:14 month:06 pages:427-452 https://dx.doi.org/10.1007/s00222-005-0438-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 161 2005 2 14 06 427-452
allfieldsGer	10.1007/s00222-005-0438-z doi (DE-627)SPR002449218 (SPR)s00222-005-0438-z-e DE-627 ger DE-627 rakwb eng Chan, Daniel verfasserin aut The minimal model program for orders over surfaces 2005 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2005 Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213 Ingalls, Colin aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 161(2005), 2 vom: 14. Juni, Seite 427-452 (DE-627)235503525 (DE-600)1398341-6 1432-1297 nnns volume:161 year:2005 number:2 day:14 month:06 pages:427-452 https://dx.doi.org/10.1007/s00222-005-0438-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 161 2005 2 14 06 427-452
allfieldsSound	10.1007/s00222-005-0438-z doi (DE-627)SPR002449218 (SPR)s00222-005-0438-z-e DE-627 ger DE-627 rakwb eng Chan, Daniel verfasserin aut The minimal model program for orders over surfaces 2005 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2005 Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213 Ingalls, Colin aut Enthalten in Inventiones mathematicae Berlin : Springer, 1966 161(2005), 2 vom: 14. Juni, Seite 427-452 (DE-627)235503525 (DE-600)1398341-6 1432-1297 nnns volume:161 year:2005 number:2 day:14 month:06 pages:427-452 https://dx.doi.org/10.1007/s00222-005-0438-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 161 2005 2 14 06 427-452
language	English
source	Enthalten in Inventiones mathematicae 161(2005), 2 vom: 14. Juni, Seite 427-452 volume:161 year:2005 number:2 day:14 month:06 pages:427-452
sourceStr	Enthalten in Inventiones mathematicae 161(2005), 2 vom: 14. Juni, Seite 427-452 volume:161 year:2005 number:2 day:14 month:06 pages:427-452
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Model Program Local Structure Minimal Model Algebraic Surface Minimal Model Program
isfreeaccess_bool	false
container_title	Inventiones mathematicae
authorswithroles_txt_mv	Chan, Daniel @@aut@@ Ingalls, Colin @@aut@@
publishDateDaySort_date	2005-06-14T00:00:00Z
hierarchy_top_id	235503525
id	SPR002449218
language_de	englisch
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author	Chan, Daniel
spellingShingle	Chan, Daniel misc Model Program misc Local Structure misc Minimal Model misc Algebraic Surface misc Minimal Model Program The minimal model program for orders over surfaces
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topic_title	The minimal model program for orders over surfaces Model Program (dpeaa)DE-He213 Local Structure (dpeaa)DE-He213 Minimal Model (dpeaa)DE-He213 Algebraic Surface (dpeaa)DE-He213 Minimal Model Program (dpeaa)DE-He213
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title	The minimal model program for orders over surfaces
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title_full	The minimal model program for orders over surfaces
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doi_str_mv	10.1007/s00222-005-0438-z
title_sort	minimal model program for orders over surfaces
title_auth	The minimal model program for orders over surfaces
abstract	Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. © Springer-Verlag 2005
abstractGer	Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. © Springer-Verlag 2005
abstract_unstemmed	Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. Combining these results yields a noncommutative version of resolution of singularities and allows us to show that any order has either a unique minimal model up to Morita equivalence or is ruled or del Pezzo. © Springer-Verlag 2005
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title_short	The minimal model program for orders over surfaces
url	https://dx.doi.org/10.1007/s00222-005-0438-z
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up_date	2024-07-04T03:03:12.877Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR002449218</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327162223.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2005 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00222-005-0438-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR002449218</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00222-005-0438-z-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chan, Daniel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The minimal model program for orders over surfaces</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2005</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag 2005</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique étale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,α) consisting of a surface Z and an element α of the Brauer group Brk(Z). We then extend the minimal model program for surfaces to such pairs. 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