Abelian varieties that split modulo all but finitely many primes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913312065716224 |
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| author | Florit, Enric |
| author_facet | Florit, Enric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abelian varieties that split modulo all but finitely many primes Florit, Enric Number Theory Algebraic Geometry 11G10, 11R52 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. |
| title | Abelian varieties that split modulo all but finitely many primes |
| topic | Number Theory Algebraic Geometry 11G10, 11R52 |
| url | https://arxiv.org/abs/2404.08496 |