## Illinois Journal of Mathematics

### Local cohomology and pure morphisms

#### 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

https://projecteuclid.org/euclid.ijm/1258735336

Digital Object Identifier
doi:10.1215/ijm/1258735336

Mathematical Reviews number (MathSciNet)
MR2346198

Zentralblatt MATH identifier
1133.13019

#### 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