A p-adic local monodromy theorem

Details A p-adic local monodromy theorem A p-adic local monodromy theorem

2001-10-11

arxiv.org/abs/math/0110124v4

preprint; published version: Annals of Math. 160 (2004), 93-184

Mathematics

Algebraic Geometry

85 pages, LaTeX2e; v2: sections 3.3, 3.4 edited to remove an error; v3: new section 2 inserted, many details added; v4 (versio

Scientific paper

We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck's local monodromy theorem (also a consequence of results of Andre and of Mebkhout). Namely, given a finite locally free sheaf on an open p-adic annulus with a connection and a compatible Frobenius structure, the corresponding module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix. Note: this preprint improves on results from our previous preprints math.AG/0102173, math.AG/0105244, math.AG/0106192, math.AG/0106193 but does not explicitly invoke any results from these preprints.

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