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arXiv · 1506.03614

On a generalization of a result of Peskine and Szpiro

Tony J. Puthenpurakal
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Abstract

Let $(R,\mathfrak{m})$ be a regular local ring containing a field $K$. Let $I$ be a Cohen-Macaulay ideal of height $g$. If $\text{char } K = p > 0$ then by a result of Peskine and Szpiro the local cohomology modules $H^i_I(R)$ vanish for $i > g$. This result is not true if $\text{char } K = 0$. However we prove that the Bass numbers of the local cohomology module $H^g_I(R)$ completely determine whether $H^i_I(R)$ vanish for $i > g$.

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Tony J. Puthenpurakal. 2015-06-11. On a generalization of a result of Peskine and Szpiro. https://arxiv.org/abs/1506.03614

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