A p-adic local monodromy theorem

• 成果类型: Article
• 署名作者: Kedlaya, KS
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2004.160.93
• 发表日期: 2004
• 页码: 93-184
• 关键词: differential-equations; index theorem; f-isocrystals; COHOMOLOGY; FINITENESS; curve

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