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Spring 2007 Constructing modules with prescribed cohomological support
Luchezar L. Avramov, Srikanth B. Iyengar
Illinois J. Math. 51(1): 1-20 (Spring 2007). DOI: 10.1215/ijm/1258735320

Abstract

A cohomological support, $\operatorname{Supp}^*_{\mathcal A}(M)$, is defined for finitely generated modules $M$ over a left noetherian ring $R$, with respect to a ring $\mathcal A$ of central cohomology operations on the derived category of $R$-modules. It is proved that if the $\mathcal A$-module $\operatorname{Ext}^*_R(M,M)$ is noetherian and $\operatorname{Ext}^*_R(M,R)=0$ for $i\gg0$, then every closed subset of $\operatorname{Supp}^*_{\mathcal A}(M)$ is the support of some finitely generated $R$-module. This theorem specializes to known realizability results for varieties of modules over group algebras, over local complete intersections, and over finite dimensional algebras over a field. The theorem is also used to produce large families of finitely generated modules of finite projective dimension over commutative local noetherian rings.

Citation

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Luchezar L. Avramov. Srikanth B. Iyengar. "Constructing modules with prescribed cohomological support." Illinois J. Math. 51 (1) 1 - 20, Spring 2007. https://doi.org/10.1215/ijm/1258735320

Information

Published: Spring 2007
First available in Project Euclid: 20 November 2009

zbMATH: 1121.13014
MathSciNet: MR2346182
Digital Object Identifier: 10.1215/ijm/1258735320

Subjects:
Primary: 13D25
Secondary: 13D05, 13H10

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

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Vol.51 • No. 1 • Spring 2007
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