Frobenius modules and de Jong's theorem

Details Frobenius modules and de Jong's theorem Frobenius modules and de Jong's theorem

2004-02-26

arxiv.org/abs/math/0402420v2

preprint; published version: Math. Res. Lett. 12 (2005), 303-320.

Mathematics

Number Theory

18 pages; v2: corrected errors in Proposition 4.3 and Lemma 5.4; to appear in Math. Res. Lett

Scientific paper

Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the possibility that an analogous theorem holds for modules with only a Frobenius structure. We show that this analogue holds in one weak formulation and fails in a second stronger formulation.

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