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Some properties and applications of $F$-finite $F$-modules
- Publication Year :
- 2010
-
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. B\"ockle to the non-$F$-finite case.<br />Comment: Material reorganized, misprints corrected, a few serious gremlins evicted
- Subjects :
- Mathematics - Commutative Algebra
Mathematics - Algebraic Geometry
13A35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1009.2668
- Document Type :
- Working Paper