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arXiv · 2012.15598

Finiteness theorems for potentially equivalent Galois representations: extension of Faltings' finiteness criteria

Plawan Das·C. S. Rajan
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Abstract

We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation $ρ$ is determined by an equality of an $m$-power character $g\mapsto Tr(ρ(g^m))$ for some natural number $m$. Using this, we extend Faltings' finiteness criteria to determine the equivalence of two $\ell$-adic, semisimple representations of the absolute Galois group of a number field, to the context of potential equivalence. We also discuss finiteness results for twist unramified representations.

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Plawan Das, C. S. Rajan. 2021-09-16. Finiteness theorems for potentially equivalent Galois representations: extension of Faltings' finiteness criteria. https://arxiv.org/abs/2012.15598

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