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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1901.05730 |
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| _version_ | 1866910688223428608 |
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| author | Goodman, Pip |
| author_facet | Goodman, Pip |
| contents | Zarhin has extensively studied restrictions placed on the endomorphism algebras of Jacobians $J$ for which the Galois group associated to their 2-torsion is insoluble and 'large' (relative to the dimension of $J$). In this paper we examine what happens when this Galois group merely contains an element of 'large' prime order. In doing so we obtain a partial converse to a result by Guralnick and Kedlaya on the endomorphism field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_05730 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Restrictions on endomorphism rings of jacobians and their minimal fields of definition Goodman, Pip Number Theory 11G10 (Primary) 14H40, 14K15 (Secondary) Zarhin has extensively studied restrictions placed on the endomorphism algebras of Jacobians $J$ for which the Galois group associated to their 2-torsion is insoluble and 'large' (relative to the dimension of $J$). In this paper we examine what happens when this Galois group merely contains an element of 'large' prime order. In doing so we obtain a partial converse to a result by Guralnick and Kedlaya on the endomorphism field. |
| title | Restrictions on endomorphism rings of jacobians and their minimal fields of definition |
| topic | Number Theory 11G10 (Primary) 14H40, 14K15 (Secondary) |
| url | https://arxiv.org/abs/1901.05730 |