Auslander-Reiten duality for Grothendieck abelian categories

Krause H (2019)
Transactions of the American Mathematical Society 371(4): 2455-2472.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Erscheinungsjahr
2019
Zeitschriftentitel
Transactions of the American Mathematical Society
Band
371
Ausgabe
4
Seite(n)
2455-2472
ISSN
0002-9947
eISSN
1088-6850
Page URI
https://pub.uni-bielefeld.de/record/2933510

Zitieren

Krause H. Auslander-Reiten duality for Grothendieck abelian categories. Transactions of the American Mathematical Society. 2019;371(4):2455-2472.
Krause, H. (2019). Auslander-Reiten duality for Grothendieck abelian categories. Transactions of the American Mathematical Society, 371(4), 2455-2472. doi:10.1090/tran/7379
Krause, H. (2019). Auslander-Reiten duality for Grothendieck abelian categories. Transactions of the American Mathematical Society 371, 2455-2472.
Krause, H., 2019. Auslander-Reiten duality for Grothendieck abelian categories. Transactions of the American Mathematical Society, 371(4), p 2455-2472.
H. Krause, “Auslander-Reiten duality for Grothendieck abelian categories”, Transactions of the American Mathematical Society, vol. 371, 2019, pp. 2455-2472.
Krause, H.: Auslander-Reiten duality for Grothendieck abelian categories. Transactions of the American Mathematical Society. 371, 2455-2472 (2019).
Krause, Henning. “Auslander-Reiten duality for Grothendieck abelian categories”. Transactions of the American Mathematical Society 371.4 (2019): 2455-2472.

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