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

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

2010-09-14

arxiv.org/abs/1009.2668v2

Mathematics

Commutative Algebra

Material reorganized, misprints corrected, a few serious gremlins evicted

Scientific paper

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. B\"ockle to the non-$F$-finite case.

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