Authors: Luchezar L. Avramov and Srikanth Iyengar

Title: Modules with prescribed cohomological support

Abstract:  

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 is shown to specialize to realizability results for varieties
of modules over group algebras, over local complete intersections,
and over finite dimensional algebras over a field.  It is also used to
produce large families of finitely generated modules of finite projective
dimension over commutative local noetherian rings.

Status: Submitted