Galois groups of low dimensional abelian varieties over finite fields
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912143824125952 |
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| author | Arango-Piñeros, Santiago Frengley, Sam Vemulapalli, Sameera |
| author_facet | Arango-Piñeros, Santiago Frengley, Sam Vemulapalli, Sameera |
| contents | We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick-Brown, we define a new invariant called the weighted permutation representation which encompasses all three of these invariants and use it to study the subtle relationships between them. We use this permutation representation to classify the triples of invariants that occur for abelian surfaces and simple abelian threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galois groups of low dimensional abelian varieties over finite fields Arango-Piñeros, Santiago Frengley, Sam Vemulapalli, Sameera Number Theory Algebraic Geometry 11G10, 14K02 We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick-Brown, we define a new invariant called the weighted permutation representation which encompasses all three of these invariants and use it to study the subtle relationships between them. We use this permutation representation to classify the triples of invariants that occur for abelian surfaces and simple abelian threefolds. |
| title | Galois groups of low dimensional abelian varieties over finite fields |
| topic | Number Theory Algebraic Geometry 11G10, 14K02 |
| url | https://arxiv.org/abs/2412.03358 |