Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Auslander-Reiten duality for Grothendieck abelian categories


Author: Henning Krause
Journal: Trans. Amer. Math. Soc. 371 (2019), 2455-2472
MSC (2010): Primary 18E15; Secondary 14F05, 16E30, 18G15
DOI: https://doi.org/10.1090/tran/7379
Published electronically: September 20, 2018
MathSciNet review: 3896086
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ \textup {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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 18E15, 14F05, 16E30, 18G15

Retrieve articles in all journals with MSC (2010): 18E15, 14F05, 16E30, 18G15


Additional Information

Henning Krause
Affiliation: Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany
Email: hkrause@math.uni-bielefeld.de

DOI: https://doi.org/10.1090/tran/7379
Received by editor(s): May 1, 2016
Received by editor(s) in revised form: August 17, 2017
Published electronically: September 20, 2018
Article copyright: © Copyright 2018 American Mathematical Society