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arXiv · 1009.2668

Some properties and applications of $F$-finite $F$-modules

Mordechai Katzman
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Abstract

The purpose of this paper is to describe several applications of finiteness properties of $F$-finite $F$-modules recently discovered by M. Hochster to the study of Frobenius maps on injective hulls, Frobenius near-splittings and to the nature of morphisms of $F$-finite $F$-modules. Among the results in the paper we show that morphisms of $F$-finite $F$-modules have a particularly simple form, and we show that certain Frobenius near-splittings have finitely many compatible submodules, thus generalizing a result of M. Blickle and G. Böckle to the non-$F$-finite case.

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Mordechai Katzman. 2011-02-03. Some properties and applications of $F$-finite $F$-modules. https://arxiv.org/abs/1009.2668

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