On vanishing of certain Ext modules

Details On vanishing of certain Ext modules On vanishing of certain Ext modules

2007-01-06

arxiv.org/abs/math/0701195v2

Mathematics

Commutative Algebra

15 pages, minor changes, to appear in Journal of the Mathematical Society of Japan

Scientific paper

Let R be a Noetherian local ring with the maximal ideal m and dim R=1. In this paper, we shall prove that the module Ext^1_R(R/Q,R) does not vanish for every parameter ideal Q in R, if the embedding dimension v(R) of R is at most 4 and the ideal m^2 kills the 0th local cohomology module H_m^0(R). The assertion is no longer true unless v(R) \leq 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.

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