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A group-theoretic generalization of the p-adic local monodromy theorem

Part of: Linear algebraic groups and related topics Algebraic number theory: local and $p$-adic fields Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  29 June 2021

Shuyang Ye
Shuyang Ye*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai, China
*
e-mail: [email protected]
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Abstract

Let G be a connected reductive group over a p-adic number field F. We propose and study the notions of G- $\varphi $ -modules and G- $(\varphi ,\nabla )$ -modules over the Robba ring, which are exact faithful F-linear tensor functors from the category of G-representations on finite-dimensional F-vector spaces to the categories of $\varphi $ -modules and $(\varphi ,\nabla )$ -modules over the Robba ring, respectively, commuting with the respective fiber functors. We study Kedlaya’s slope filtration theorem in this context, and show that G- $(\varphi ,\nabla )$ -modules over the Robba ring are “G-quasi-unipotent,” which is a generalization of the p-adic local monodromy theorem proved independently by Y. André, K. S. Kedlaya, and Z. Mebkhout.

Keywords

Robba ringp-adic local monodromy theoremreductive groups

MSC classification

Primary: 11S85: Other nonanalytic theory
Secondary: 20G25: Linear algebraic groups over local fields and their integers 17B45: Lie algebras of linear algebraic groups
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 5 , October 2022 , pp. 1450 - 1485
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

This paper is partially supported by a research grant from Shanghai Key Laboratory of PMMP 18dz2271000.

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