On vanishing of certain Ext modules
GOTO, Shiro ; HAYASAKA, Futoshi ; TAKAHASHI, Ryo
J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 1045-1064 / Harvested from Project Euclid
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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 $\Ext^1_R (R/Q, R)$ 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 $\m^2$ kills the $0^{\underline{th}}$ local cohomology module $H_{\mathfrak{m}}^0(R)$ . The assertion is no longer true unless $\mathrm{v}(R) \leq 4$ . Counterexamples are given. We shall also discuss the relation between our counterexamples and a problem on modules of finite G-dimension.
Publié le : 2008-10-15
Classification:  vanishing of Ext,  parameter ideal,  G-dimension,  13D07,  13D05 
@article{1225894032,
     author = {GOTO, Shiro and HAYASAKA, Futoshi and TAKAHASHI, Ryo},
     title = {On vanishing of certain Ext modules},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 1045-1064},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1225894032}
}

GOTO, Shiro; HAYASAKA, Futoshi; TAKAHASHI, Ryo. On vanishing of certain Ext modules. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  1045-1064. http://gdmltest.u-ga.fr/item/1225894032/