Summary: CONSTRUCTING MODULES WITH PRESCRIBED
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 A-module Ext
R(M, M) is noetherian
R(M, R) = 0 for i 0, then every closed subset of Supp
is the support of some finitely generated R-module. 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.