1. AUSLANDER-REITEN DUALITY FOR GROTHENDIECK ABELIAN CATEGORIES.
- Author
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KRAUSE, HENNING
- Subjects
- *
DUALITY theory (Mathematics) , *MODULES (Algebra) , *CATEGORIES (Mathematics) , *ENDOMORPHISM rings , *GEOMETRIC connections - 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]
- Published
- 2019
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