Constructing modules with prescribed cohomological support
摘要
A cohomological support, Supp_A(M), is defined for finitely generated modules M over an left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the A-module Ext^R(M,M) is noetherian and Ext_i^R(M,R)=0 for i>>0, then every closed subset of Supp_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.
引用
@article{arxiv.math/0702654,
title = {Constructing modules with prescribed cohomological support},
author = {Luchezar L. Avramov and Srikanth B. Iyengar},
journal= {arXiv preprint arXiv:math/0702654},
year = {2007}
}
备注
To appear in the Illinois Journal of Mathematics, the issue honoring Phillip Griffith. Revised version has 18 pages. A word (the first one) has been added to the title and the material has been reorganized into seven sections, in place of the original six. There are, however, no changes of any substance