A group-theoretic generalization of the p-adic local monodromy theorem
Canadian journal of mathematics, Tome 74 (2022) no. 5, pp. 1450-1485
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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.
Mots-clés :
Robba ring, p-adic local monodromy theorem, reductive groups
Ye, Shuyang. A group-theoretic generalization of the p-adic local monodromy theorem. Canadian journal of mathematics, Tome 74 (2022) no. 5, pp. 1450-1485. doi: 10.4153/S0008414X21000328
@article{10_4153_S0008414X21000328,
author = {Ye, Shuyang},
title = {A group-theoretic generalization of the p-adic local monodromy theorem},
journal = {Canadian journal of mathematics},
pages = {1450--1485},
year = {2022},
volume = {74},
number = {5},
doi = {10.4153/S0008414X21000328},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000328/}
}
TY - JOUR AU - Ye, Shuyang TI - A group-theoretic generalization of the p-adic local monodromy theorem JO - Canadian journal of mathematics PY - 2022 SP - 1450 EP - 1485 VL - 74 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000328/ DO - 10.4153/S0008414X21000328 ID - 10_4153_S0008414X21000328 ER -
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