Illinois Journal of Mathematics

Local cohomology and pure morphisms

Anurag K. Singh and Uli Walther

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Abstract

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

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

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735336

Digital Object Identifier
doi:10.1215/ijm/1258735336

Mathematical Reviews number (MathSciNet)
MR2346198

Zentralblatt MATH identifier
1133.13019

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

Citation

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


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