A p-adic local monodromy theorem

By Kiran S. Kedlaya. 2001

64 citations recorded by the source corpus.

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 module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b5326b3b584ccb34876da0103c0975d3d467aa32

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Citations in the corpus

Geometrization of the local Langlands correspondence (2021, background): “Kedlaya [10] classified φ-modules over R, and the “expanding” property of Frobenius implies φ ModR Vector Bundles on X .”
Semistable reduction for overconvergent $F$-isocrystals I: Unipotence and logarithmic extensions (2004, unknown): “We conclude with a form of the p-adic local monodromy theorem of [1, 22, 27] (formerly known as Crew’s conjecture or the Crew-Tsuzuki conjecture).”
Slope filtrations for relative Frobenius (2006, background): “…de filtration par les pentes donne un analogue partiel de la décomposition en espaces propres d'une transformation linéaire, pour un endomorphisme semilinéaire (pour Frobenius) d'un module libre de type fini sur l'anneau de Robba (l'anneau des germes de fonctions analytiques rigides sur une…”
Slope filtrations revisited (2005, background): “1.1 The slope filtration theorem . . . . . . . . . . . . . . . . . . . . . . . . . .”
Period spaces for Hodge structures in equal characteristic (2005, unknown): “The later is a powerful tool that has given rise to proofs of various famous conjectures, like the conjectures that “weakly admissible implies admissible” [6, 42], that “de Rham implies potentially semistable” [5, 41], or Crew’s conjecture which is also called the p-adic local monodromy theorem [40]”