On vanishing of certain Ext modules
Commutative Algebra
2008-07-08 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0701195,
title = {On vanishing of certain Ext modules},
author = {Shiro Goto and Futoshi Hayasaka and Ryo Takahashi},
journal= {arXiv preprint arXiv:math/0701195},
year = {2008}
}
Comments
15 pages, minor changes, to appear in Journal of the Mathematical Society of Japan