Congruences of Galois representations attached to effective \(A\)-motives over global function fields

This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be i...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Author: Okumura, Yoshiaki
Format: Article
Language:English
Subjects:
Congruences
Criteria
Number theory
Representations
Online Access:Get full text
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Summary:This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of \(K\). This is a function field analog of Ozeki-Taguchi's criterion for \(\ell\)-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective \(A\)-motives with some constrained.
ISSN:2331-8422