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On vanishing of certain Ext modules

Shiro Goto·Futoshi Hayasaka·Ryo Takahashi
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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.

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Shiro Goto, Futoshi Hayasaka, Ryo Takahashi. 2008-07-08. On vanishing of certain Ext modules. https://arxiv.org/abs/math/0701195

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