 
Summary: CONSTRUCTING MODULES WITH PRESCRIBED
COHOMOLOGICAL SUPPORT
LUCHEZAR L. AVRAMOV AND SRIKANTH B. IYENGAR
To Phil Griffith, algebraist and friend.
Abstract. A cohomological support, Supp
A(M), is defined for finitely
generated modules M over a 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 Amodule Ext
R(M, M) is noetherian
and Ext
R(M, R) = 0 for i 0, then every closed subset of Supp
A(M)
is the support of some finitely generated Rmodule. This theorem spe
cializes 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 fam
ilies of finitely generated modules of finite projective dimension over
commutative local noetherian rings.
Introduction
