A p-adic local monodromy theorem
摘要
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.
引用
@article{arxiv.math/0110124,
title = {A p-adic local monodromy theorem},
author = {Kiran S. Kedlaya},
journal= {arXiv preprint arXiv:math/0110124},
year = {2007}
}
备注
85 pages, LaTeX2e; v2: sections 3.3, 3.4 edited to remove an error; v3: new section 2 inserted, many details added; v4 (version for publication): introduction expanded, small errors fixed. To appear in Annals of Mathematics