Monodromy representations of p-adic differential equations in families

2022/09/01 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2209.00593

openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a relative version of the local monodromy theorem for ordinary differential equations on an annulus over a mixed-characteristic nonarchimedean field, and give several applications in p-adic cohomology and p-adic Hodge theory. These include a simplified proof of the semistable reduction theorem for overconvergent F-isocrystals, a relative version of Berger's theorem that de Rham representations are potentially semistable, and a multivariate version of the local monodromy theorem in the style of Drinfeld's lemma on fundamental groups.

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