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

2022/04/19 by Okumura, Yoshiaki · 1 citation
#11F80 #11R58 #FOS: Mathematics #Number Theory (math.NT) #Primary 11G09 #Secondary 13A35

paper · doi:10.48550/arxiv.2204.08639

Abstract

This article investigates congruences of \mathfrakp-adic representations arising from effective A-motives defined over a global function field K. We give a criterion for two congruent \mathfrakp-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 ℓ-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.

Cited by

• Torsion of rank-two A-motives values in odd characteristic cyclotomic towers

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