Sign involutions on para-abelian varieties
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929328150806528 |
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| author | Bergqvist, Jakob Dang, Thuong Schröer, Stefan |
| author_facet | Bergqvist, Jakob Dang, Thuong Schröer, Stefan |
| contents | We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil--Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer--Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03314 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sign involutions on para-abelian varieties Bergqvist, Jakob Dang, Thuong Schröer, Stefan Algebraic Geometry 14L30, 14K15, 14K30, 14J26 We study the so-called sign involutions on twisted forms of abelian varieties, and show that such a sign involution exists if and only if the class in the Weil--Châtelet group is annihilated by two. If these equivalent conditions hold, we prove that the Picard scheme of the quotient is étale and contains no points of finite order. In dimension one, such quotients are Brauer--Severi curves, and we analyze the ensuing embeddings of the genus-one curve into twisted forms of Hirzebruch surfaces and weighted projective spaces. |
| title | Sign involutions on para-abelian varieties |
| topic | Algebraic Geometry 14L30, 14K15, 14K30, 14J26 |
| url | https://arxiv.org/abs/2301.03314 |