Abelian varieties that split modulo all but finitely many primes
| Autor: | Florit, Enric |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages, comments are welcome! |
| Databáze: | arXiv |
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