The Nakayama functor and its completion for Gorenstein algebras
Iyengar SB, Krause H (2022)
Bulletin de la SMF (Société Mathématique de France) 150(2): 347-391.
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Autor*in
Iyengar, Srikanth B.;
Krause, HenningUniBi 
Einrichtung
Abstract / Bemerkung
Duality properties are studied for a Gorenstein algebra that is finite and projective over its center. Using the homotopy category of injective modules, it is proved that there is a local duality theorem for the subcategory of acyclic complexes of such an algebra, akin to the local duality theorems of Grothendieck and Serre in the context of commutative algebra and algebraic geometry. A key ingredient is the Nakayama functor on the bounded derived category of a Gorenstein algebra and its extension to the full homotopy category of injective modules.
Stichworte
Gorenstein algebra;
Gorenstein-projective module;
local duality;
Nakayma;
functor;
Serre duality;
stable module category
Erscheinungsjahr
2022
Zeitschriftentitel
Bulletin de la SMF (Société Mathématique de France)
Band
150
Ausgabe
2
Seite(n)
347-391
ISSN
0037-9484
eISSN
2102-622X
Page URI
https://pub.uni-bielefeld.de/record/2966111
Zitieren
Iyengar SB, Krause H. The Nakayama functor and its completion for Gorenstein algebras. Bulletin de la SMF (Société Mathématique de France) . 2022;150(2):347-391.
Iyengar, S. B., & Krause, H. (2022). The Nakayama functor and its completion for Gorenstein algebras. Bulletin de la SMF (Société Mathématique de France) , 150(2), 347-391. https://doi.org/10.24033/bsmf.2849
Iyengar, Srikanth B., and Krause, Henning. 2022. “The Nakayama functor and its completion for Gorenstein algebras”. Bulletin de la SMF (Société Mathématique de France) 150 (2): 347-391.
Iyengar, S. B., and Krause, H. (2022). The Nakayama functor and its completion for Gorenstein algebras. Bulletin de la SMF (Société Mathématique de France) 150, 347-391.
Iyengar, S.B., & Krause, H., 2022. The Nakayama functor and its completion for Gorenstein algebras. Bulletin de la SMF (Société Mathématique de France) , 150(2), p 347-391.
S.B. Iyengar and H. Krause, “The Nakayama functor and its completion for Gorenstein algebras”, Bulletin de la SMF (Société Mathématique de France) , vol. 150, 2022, pp. 347-391.
Iyengar, S.B., Krause, H.: The Nakayama functor and its completion for Gorenstein algebras. Bulletin de la SMF (Société Mathématique de France) . 150, 347-391 (2022).
Iyengar, Srikanth B., and Krause, Henning. “The Nakayama functor and its completion for Gorenstein algebras”. Bulletin de la SMF (Société Mathématique de France) 150.2 (2022): 347-391.
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arXiv: 2010.05676
Preprint: 10.48550/arXiv.2010.05676
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