Illinois Journal of Mathematics

Local cohomology and pure morphisms

Anurag K. Singh and Uli Walther

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We study a question raised by Eisenbud, Mustaţa, and Stillman regarding the injectivity of natural maps from $\Ext$ modules to local cohomology modules. We obtain some positive answers to this question which extend earlier results of Lyubeznik. In the process, we also prove a vanishing theorem for local cohomology modules which connects theorems previously known in the case of positive characteristic and in the case of monomial ideals.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 287-298.

First available in Project Euclid: 20 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]


Singh, Anurag K.; Walther, Uli. Local cohomology and pure morphisms. Illinois J. Math. 51 (2007), no. 1, 287--298. doi:10.1215/ijm/1258735336.

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