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AUSLANDER-REITEN DUALITY FOR GROTHENDIECK ABELIAN CATEGORIES.
- Source :
-
Transactions of the American Mathematical Society . 2/15/2019, Vol. 371 Issue 4, p2455-2472. 18p. - Publication Year :
- 2019
-
Abstract
- Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext¹(C,−) into modules over the endomorphism ring of C admits a partially defined right adjoint when C is a finitely presented object. This result seems to be new even for module categories. For appropriate schemes over a field, the connection with Serre duality is discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 371
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 134011744
- Full Text :
- https://doi.org/10.1090/tran/7379