Generalized local cohomology and the canonical element conjecture

Abstract

We study a generalization of the Canonical Element Conjecture. In particular we show that given a nonregular local ring (A, m) and an i > 0, there exist finitely generated A-modules M such that the canonical map from Ext i A (M/mM, Syz i (M/mM)) to H i m (M, Syz i (M/mM)) is nonzero. Moreover, we show that even when M has an infinite projective dimension and i > dim(A), studying these maps sheds light on the Canonical Element Conjecture.