Let be a Noetherian local ring with the maximal ideal and . In this paper, we shall prove that the module does not vanish for every parameter ideal in , if the embedding dimension of is at most and the ideal kills the local cohomology module . The assertion is no longer true unless . Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.
Shiro GOTO. Futoshi HAYASAKA. Ryo TAKAHASHI. "On vanishing of certain Ext modules." J. Math. Soc. Japan 60 (4) 1045 - 1064, October, 2008. https://doi.org/10.2969/jmsj/06041045