On vanishing of certain Ext modules

抄録

Let R be a Noetherian local ring with the maximal ideal \mathfrak{m} and dim R = 1. In this paper, we shall prove that the module Ext¹_R (R/Q, R) does not vanish for every parameter ideal Q in R, if the embedding dimension \mathrm{v}(R) of R is at most 4 and the ideal \mathfrak{m}² kills the 0^{\underline{th}} local cohomology module H_\mathfrak{m}⁰(R). The assertion is no longer true unless v(R) ≤ 4. Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.