Liftable derived equivalences and objective categories

We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tiltin...
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Autor*in:	Chen, Xiaofa [verfasserIn] Chen, Xiao-Wu [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020
Ausgabe:	Version of Record online: 22 June 2020

Anmerkung:	Last seen: 10.03.2023

Übergeordnetes Werk:	Enthalten in: Bulletin of the London Mathematical Society - London Mathematical Society, Hoboken, NJ : Wiley, 1969, Volume 52(2020), Issue 5, pp. 816-834
Übergeordnetes Werk:	volume:52 ; year:2020 ; number:5 ; pages:816-834

Links:	Full Text at Publisher

DOI / URN:	10.1112/blms.12364

Katalog-ID:	1838874542

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520			\|a We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor.
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allfields	10.1112/blms.12364 doi (DE-627)1838874542 (DE-599)KXP1838874542 DE-627 ger DE-627 rda eng 16D90 16G10 18F30 msc Chen, Xiaofa verfasserin aut Liftable derived equivalences and objective categories Version of Record online: 22 June 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 10.03.2023 We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Chen, Xiao-Wu verfasserin aut Enthalten in London Mathematical Society Bulletin of the London Mathematical Society Hoboken, NJ : Wiley, 1969 Volume 52(2020), Issue 5, pp. 816-834 Online-Ressource (DE-627)270132023 (DE-600)1476985-2 (DE-576)078129966 1469-2120 nnns volume:52 year:2020 number:5 pages:816-834 https://doi.org/10.1112/blms.12364 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_65 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 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_2034 GBV_ILN_2037 GBV_ILN_2038 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_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 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_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 52 2020 5 816-834 Volume 52(2020), Issue 5, pp. 816-834 2088 01 DE-Frei3c 4287040783 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: [...] The paper was revised when the second author visited University of Bielefeld, with a research stay partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach. l01 10-03-23 2088 01 DE-Frei3c 00 (DE-627)1294704400 AMS:16 Associative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294704397 AMS:18 Category theory; homological algebra
spelling	10.1112/blms.12364 doi (DE-627)1838874542 (DE-599)KXP1838874542 DE-627 ger DE-627 rda eng 16D90 16G10 18F30 msc Chen, Xiaofa verfasserin aut Liftable derived equivalences and objective categories Version of Record online: 22 June 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 10.03.2023 We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Chen, Xiao-Wu verfasserin aut Enthalten in London Mathematical Society Bulletin of the London Mathematical Society Hoboken, NJ : Wiley, 1969 Volume 52(2020), Issue 5, pp. 816-834 Online-Ressource (DE-627)270132023 (DE-600)1476985-2 (DE-576)078129966 1469-2120 nnns volume:52 year:2020 number:5 pages:816-834 https://doi.org/10.1112/blms.12364 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_65 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 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_2034 GBV_ILN_2037 GBV_ILN_2038 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_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 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_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 52 2020 5 816-834 Volume 52(2020), Issue 5, pp. 816-834 2088 01 DE-Frei3c 4287040783 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: [...] The paper was revised when the second author visited University of Bielefeld, with a research stay partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach. l01 10-03-23 2088 01 DE-Frei3c 00 (DE-627)1294704400 AMS:16 Associative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294704397 AMS:18 Category theory; homological algebra
allfields_unstemmed	10.1112/blms.12364 doi (DE-627)1838874542 (DE-599)KXP1838874542 DE-627 ger DE-627 rda eng 16D90 16G10 18F30 msc Chen, Xiaofa verfasserin aut Liftable derived equivalences and objective categories Version of Record online: 22 June 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 10.03.2023 We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Chen, Xiao-Wu verfasserin aut Enthalten in London Mathematical Society Bulletin of the London Mathematical Society Hoboken, NJ : Wiley, 1969 Volume 52(2020), Issue 5, pp. 816-834 Online-Ressource (DE-627)270132023 (DE-600)1476985-2 (DE-576)078129966 1469-2120 nnns volume:52 year:2020 number:5 pages:816-834 https://doi.org/10.1112/blms.12364 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_65 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 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_2034 GBV_ILN_2037 GBV_ILN_2038 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_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 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_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 52 2020 5 816-834 Volume 52(2020), Issue 5, pp. 816-834 2088 01 DE-Frei3c 4287040783 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: [...] The paper was revised when the second author visited University of Bielefeld, with a research stay partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach. l01 10-03-23 2088 01 DE-Frei3c 00 (DE-627)1294704400 AMS:16 Associative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294704397 AMS:18 Category theory; homological algebra
allfieldsGer	10.1112/blms.12364 doi (DE-627)1838874542 (DE-599)KXP1838874542 DE-627 ger DE-627 rda eng 16D90 16G10 18F30 msc Chen, Xiaofa verfasserin aut Liftable derived equivalences and objective categories Version of Record online: 22 June 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 10.03.2023 We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Chen, Xiao-Wu verfasserin aut Enthalten in London Mathematical Society Bulletin of the London Mathematical Society Hoboken, NJ : Wiley, 1969 Volume 52(2020), Issue 5, pp. 816-834 Online-Ressource (DE-627)270132023 (DE-600)1476985-2 (DE-576)078129966 1469-2120 nnns volume:52 year:2020 number:5 pages:816-834 https://doi.org/10.1112/blms.12364 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_65 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 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_2034 GBV_ILN_2037 GBV_ILN_2038 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_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 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_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 52 2020 5 816-834 Volume 52(2020), Issue 5, pp. 816-834 2088 01 DE-Frei3c 4287040783 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: [...] The paper was revised when the second author visited University of Bielefeld, with a research stay partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach. l01 10-03-23 2088 01 DE-Frei3c 00 (DE-627)1294704400 AMS:16 Associative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294704397 AMS:18 Category theory; homological algebra
allfieldsSound	10.1112/blms.12364 doi (DE-627)1838874542 (DE-599)KXP1838874542 DE-627 ger DE-627 rda eng 16D90 16G10 18F30 msc Chen, Xiaofa verfasserin aut Liftable derived equivalences and objective categories Version of Record online: 22 June 2020 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Last seen: 10.03.2023 We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Chen, Xiao-Wu verfasserin aut Enthalten in London Mathematical Society Bulletin of the London Mathematical Society Hoboken, NJ : Wiley, 1969 Volume 52(2020), Issue 5, pp. 816-834 Online-Ressource (DE-627)270132023 (DE-600)1476985-2 (DE-576)078129966 1469-2120 nnns volume:52 year:2020 number:5 pages:816-834 https://doi.org/10.1112/blms.12364 Resolving-System Full Text at Publisher lizenzpflichtig GBV_USEFLAG_U GBV_ILN_2088 ISIL_DE-Frei3c SYSFLAG_1 GBV_KXP 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_65 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_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_266 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_2034 GBV_ILN_2037 GBV_ILN_2038 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_2068 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2113 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_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 52 2020 5 816-834 Volume 52(2020), Issue 5, pp. 816-834 2088 01 DE-Frei3c 4287040783 00 --%%-- --%%-- --%%-- n Funding text/Acknowledgements: [...] The paper was revised when the second author visited University of Bielefeld, with a research stay partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach. l01 10-03-23 2088 01 DE-Frei3c 00 (DE-627)1294704400 AMS:16 Associative rings and algebras 2088 01 DE-Frei3c 00 (DE-627)1294704397 AMS:18 Category theory; homological algebra
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title_auth	Liftable derived equivalences and objective categories
abstract	We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Last seen: 10.03.2023
abstractGer	We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Last seen: 10.03.2023
abstract_unstemmed	We give two proofs of the following theorem and a partial generalization: if a finite-dimensional algebraAis derived equivalent to a smooth projective scheme, then any derived equivalence betweenAand another algebraBis standard, that is, isomorphic to the derived tensor functor by a two-sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-identity and a liftable derived equivalence; (3) the derived category of coherent sheaves on a certain class of projective schemes is triangle-objective, that is, any triangle autoequivalence on it, which preserves the isomorphism classes of all objects, is necessarily isomorphic to the identity functor. Last seen: 10.03.2023
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container_issue	5
title_short	Liftable derived equivalences and objective categories
url	https://doi.org/10.1112/blms.12364
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author2	Chen, Xiao-Wu
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doi_str	10.1112/blms.12364
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up_date	2024-07-04T10:20:14.449Z
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