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arXiv · 2006.06737

Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible $\ell$-adic Galois Representation

Lambert A'Campo
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Abstract

Let $K$ be a complete, discretely valued field with finite residue field and $G_K$ its absolute Galois group. The subject of this note is the study of the set of positive integers $d$ for which there exists an absolutely irreducible $\ell$-adic representation of $G_K$ of dimension $d$ with rational traces on inertia. Our main result is that non-Sophie Germain primes are not in this set when the residue characteristic of $K$ is $> 3$. The result stated in the title is a special case.

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Lambert A'Campo. 2020-06-11. Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible $\ell$-adic Galois Representation. https://doi.org/10.1112/blms.12472

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