2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917297401102336 |
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| author | Dogra, Netan |
| author_facet | Dogra, Netan |
| contents | This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second étale cohomology of the Jacobian of a hyperelliptic curve with a rational Weierstrass point. In particular, this can give a method to determine the rational points on such curves via the Chabauty--Coleman--Kim method. This is applied to answer a question of Bugeaud, Mignotte, Siksek, Stoll and Tengely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04996 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I Dogra, Netan Number Theory Algebraic Geometry This paper introduces explicit Galois cohomological methods for determining the ranks of Bloch--Kato Selmer groups associated to the Tate twists of the 2-adic second étale cohomology of the Jacobian of a hyperelliptic curve with a rational Weierstrass point. In particular, this can give a method to determine the rational points on such curves via the Chabauty--Coleman--Kim method. This is applied to answer a question of Bugeaud, Mignotte, Siksek, Stoll and Tengely. |
| title | 2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves I |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2312.04996 |