Auslander-Reiten duality for Grothendieck abelian categories
Representation Theory
2016-04-12 v1 Algebraic Geometry
Category Theory
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 Ext^1(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.
Keywords
Cite
@article{arxiv.1604.02813,
title = {Auslander-Reiten duality for Grothendieck abelian categories},
author = {Henning Krause},
journal= {arXiv preprint arXiv:1604.02813},
year = {2016}
}
Comments
16 pages