Constructing modules with prescribed cohomological support

Details Constructing modules with prescribed cohomological support Constructing modules with prescribed cohomological support

2007-02-22

arxiv.org/abs/math/0702654v2

Mathematics

Rings and Algebras

To appear in the Illinois Journal of Mathematics, the issue honoring Phillip Griffith. Revised version has 18 pages. A word (t

Scientific paper

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.

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