Title
Dualizing complexes of noetherian complete algebras via coalgebras Dualizing complexes of noetherian complete algebras via coalgebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Communications in algebra. - New York, N.Y.
Volume/pages
42(2014) :1 , p. 271-285
ISSN
0092-7872
ISI
000325788500020
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Let A be a noetherian complete basic semiperfect algebra over an algebraically closed field, and C=A degrees be its dual coalgebra. If A is Artin-Schelter regular, then the local cohomology of A is isomorphic to a shift of twisted bimodule C-1(sigma*) with sigma a coalgebra automorphism. This yields that the balanced dualinzing complex of A is a shift of the twisted bimodule (sigma*)A(1). If sigma is an inner automorphism, then A is Calabi-Yau. An appendix is included to prove a duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra.
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