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arXiv · 2404.08496

Abelian varieties that split modulo all but finitely many primes

Enric Florit
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Abstract

Let $A$ be a simple abelian variety over a number field $k$ such that $\operatorname{End}(A)$ is noncommutative. We show that $A$ splits modulo all but finitely many primes of $k$. We prove this by considering the subalgebras of $\operatorname{End}(A_{\mathfrak p})\otimes\mathbb{Q}$ which have prime Schur index. Our main tools are Tate's characterization of endomorphism algebras of abelian varieties over finite fields, and a Theorem of Chia-Fu Yu on embeddings of simple algebras.

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Enric Florit. 2024-04-12. Abelian varieties that split modulo all but finitely many primes. https://arxiv.org/abs/2404.08496

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