Semistable abelian varieties over ℚ

Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Calegari, Frank [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2004

Schlagwörter:	Recent Result Abelian Variety Good Reduction Semistable Abelian Variety Discriminant Bound

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2004

Übergeordnetes Werk:	Enthalten in: Manuscripta mathematica - Berlin : Springer, 1969, 113(2004), 4 vom: 03. März, Seite 507-529
Übergeordnetes Werk:	volume:113 ; year:2004 ; number:4 ; day:03 ; month:03 ; pages:507-529

Links:	Volltext

DOI / URN:	10.1007/s00229-004-0445-1

Katalog-ID:	SPR002600927

Internformat


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520			\|a Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}.
650		4	\|a Recent Result \|7 (dpeaa)DE-He213
650		4	\|a Abelian Variety \|7 (dpeaa)DE-He213
650		4	\|a Good Reduction \|7 (dpeaa)DE-He213
650		4	\|a Semistable Abelian Variety \|7 (dpeaa)DE-He213
650		4	\|a Discriminant Bound \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
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_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
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
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912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
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952			\|d 113 \|j 2004 \|e 4 \|b 03 \|c 03 \|h 507-529

Indexfelder

author_variant	f c fc
matchkey_str	article:14321785:2004----::eitbeblavr
hierarchy_sort_str	2004
publishDate	2004
allfields	10.1007/s00229-004-0445-1 doi (DE-627)SPR002600927 (SPR)s00229-004-0445-1-e DE-627 ger DE-627 rakwb eng Calegari, Frank verfasserin aut Semistable abelian varieties over ℚ 2004 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213 Enthalten in Manuscripta mathematica Berlin : Springer, 1969 113(2004), 4 vom: 03. März, Seite 507-529 (DE-627)253770637 (DE-600)1459409-2 1432-1785 nnns volume:113 year:2004 number:4 day:03 month:03 pages:507-529 https://dx.doi.org/10.1007/s00229-004-0445-1 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_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_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 113 2004 4 03 03 507-529
spelling	10.1007/s00229-004-0445-1 doi (DE-627)SPR002600927 (SPR)s00229-004-0445-1-e DE-627 ger DE-627 rakwb eng Calegari, Frank verfasserin aut Semistable abelian varieties over ℚ 2004 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213 Enthalten in Manuscripta mathematica Berlin : Springer, 1969 113(2004), 4 vom: 03. März, Seite 507-529 (DE-627)253770637 (DE-600)1459409-2 1432-1785 nnns volume:113 year:2004 number:4 day:03 month:03 pages:507-529 https://dx.doi.org/10.1007/s00229-004-0445-1 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_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_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 113 2004 4 03 03 507-529
allfields_unstemmed	10.1007/s00229-004-0445-1 doi (DE-627)SPR002600927 (SPR)s00229-004-0445-1-e DE-627 ger DE-627 rakwb eng Calegari, Frank verfasserin aut Semistable abelian varieties over ℚ 2004 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213 Enthalten in Manuscripta mathematica Berlin : Springer, 1969 113(2004), 4 vom: 03. März, Seite 507-529 (DE-627)253770637 (DE-600)1459409-2 1432-1785 nnns volume:113 year:2004 number:4 day:03 month:03 pages:507-529 https://dx.doi.org/10.1007/s00229-004-0445-1 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_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_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 113 2004 4 03 03 507-529
allfieldsGer	10.1007/s00229-004-0445-1 doi (DE-627)SPR002600927 (SPR)s00229-004-0445-1-e DE-627 ger DE-627 rakwb eng Calegari, Frank verfasserin aut Semistable abelian varieties over ℚ 2004 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213 Enthalten in Manuscripta mathematica Berlin : Springer, 1969 113(2004), 4 vom: 03. März, Seite 507-529 (DE-627)253770637 (DE-600)1459409-2 1432-1785 nnns volume:113 year:2004 number:4 day:03 month:03 pages:507-529 https://dx.doi.org/10.1007/s00229-004-0445-1 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_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_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 113 2004 4 03 03 507-529
allfieldsSound	10.1007/s00229-004-0445-1 doi (DE-627)SPR002600927 (SPR)s00229-004-0445-1-e DE-627 ger DE-627 rakwb eng Calegari, Frank verfasserin aut Semistable abelian varieties over ℚ 2004 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2004 Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213 Enthalten in Manuscripta mathematica Berlin : Springer, 1969 113(2004), 4 vom: 03. März, Seite 507-529 (DE-627)253770637 (DE-600)1459409-2 1432-1785 nnns volume:113 year:2004 number:4 day:03 month:03 pages:507-529 https://dx.doi.org/10.1007/s00229-004-0445-1 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_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_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 113 2004 4 03 03 507-529
language	English
source	Enthalten in Manuscripta mathematica 113(2004), 4 vom: 03. März, Seite 507-529 volume:113 year:2004 number:4 day:03 month:03 pages:507-529
sourceStr	Enthalten in Manuscripta mathematica 113(2004), 4 vom: 03. März, Seite 507-529 volume:113 year:2004 number:4 day:03 month:03 pages:507-529
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Recent Result Abelian Variety Good Reduction Semistable Abelian Variety Discriminant Bound
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container_title	Manuscripta mathematica
authorswithroles_txt_mv	Calegari, Frank @@aut@@
publishDateDaySort_date	2004-03-03T00:00:00Z
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author	Calegari, Frank
spellingShingle	Calegari, Frank misc Recent Result misc Abelian Variety misc Good Reduction misc Semistable Abelian Variety misc Discriminant Bound Semistable abelian varieties over ℚ
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topic_title	Semistable abelian varieties over ℚ Recent Result (dpeaa)DE-He213 Abelian Variety (dpeaa)DE-He213 Good Reduction (dpeaa)DE-He213 Semistable Abelian Variety (dpeaa)DE-He213 Discriminant Bound (dpeaa)DE-He213
topic	misc Recent Result misc Abelian Variety misc Good Reduction misc Semistable Abelian Variety misc Discriminant Bound
topic_unstemmed	misc Recent Result misc Abelian Variety misc Good Reduction misc Semistable Abelian Variety misc Discriminant Bound
topic_browse	misc Recent Result misc Abelian Variety misc Good Reduction misc Semistable Abelian Variety misc Discriminant Bound
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Semistable abelian varieties over ℚ
ctrlnum	(DE-627)SPR002600927 (SPR)s00229-004-0445-1-e
title_full	Semistable abelian varieties over ℚ
author_sort	Calegari, Frank
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author_browse	Calegari, Frank
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author-letter	Calegari, Frank
doi_str_mv	10.1007/s00229-004-0445-1
title_sort	semistable abelian varieties over ℚ
title_auth	Semistable abelian varieties over ℚ
abstract	Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. © Springer-Verlag Berlin Heidelberg 2004
abstractGer	Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. © Springer-Verlag Berlin Heidelberg 2004
abstract_unstemmed	Abstract. We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}. © Springer-Verlag Berlin Heidelberg 2004
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title_short	Semistable abelian varieties over ℚ
url	https://dx.doi.org/10.1007/s00229-004-0445-1
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up_date	2024-07-03T14:01:32.190Z
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We prove that for N=6 and N=10, there do not exist any non-zero semistable abelian varieties over ℚ with good reduction outside primes dividing N. Our results are contingent on the GRH discriminant bounds of Odlyzko. Combined with recent results of Brumer-Kramer and of Schoof, this result is best possible: if N is squarefree, there exists a non-zero semistable abelian variety over ℚ with good reduction outside primes dividing N precisely when N∉{1,2,3,5,6,7,10,13}.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Recent Result</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Abelian Variety</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Good Reduction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Semistable Abelian Variety</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Discriminant Bound</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Manuscripta mathematica</subfield><subfield code="d">Berlin : Springer, 1969</subfield><subfield code="g">113(2004), 4 vom: 03. 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Semistable abelian varieties over ℚ

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