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arXiv · 1210.8387

The category of F-modules has finite global dimension

Linquan Ma
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Abstract

Let R be a regular ring of characteristic p. Hochster showed that the category of Lyubeznik's F-modules has enough injectives, so that every F-module has an injective resolution in this category. We show that under mild conditions on R, for example when R is essentially of finite type over an F-finite regular local ring, the category of F-modules has finite global dimension d+1 where d=dimR. We also give examples to show that for F-finite F-modules, $\Ext_{F_R}^1(M,N)$ need not be finite.

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Linquan Ma. 2013-07-04. The category of F-modules has finite global dimension. https://arxiv.org/abs/1210.8387

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