Non-abelian descent types
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909295448162304 |
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| author | Linh, Nguyen Manh |
| author_facet | Linh, Nguyen Manh |
| contents | We present the notion of non-abelian descent type, which classifies torsors up to twisting by a Galois cocycle. This relies on the previous construction of kernels and non-abelian Galois 2-cohomology due to Springer and Borovoi. The necessity of descent types arises in the context of the descent theory where no torsors are given a priori, for example, when we wish to study the arithmetic properties such as the Brauer--Manin obstruction to the Hasse principle on homogeneous spaces without rational points. This new definition also unifies the types by Colliot-Thélène--Sansuc, the extended types by Harari--Skorobogatov, and the finite descent type by Harpaz--Wittenberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-abelian descent types Linh, Nguyen Manh Algebraic Geometry We present the notion of non-abelian descent type, which classifies torsors up to twisting by a Galois cocycle. This relies on the previous construction of kernels and non-abelian Galois 2-cohomology due to Springer and Borovoi. The necessity of descent types arises in the context of the descent theory where no torsors are given a priori, for example, when we wish to study the arithmetic properties such as the Brauer--Manin obstruction to the Hasse principle on homogeneous spaces without rational points. This new definition also unifies the types by Colliot-Thélène--Sansuc, the extended types by Harari--Skorobogatov, and the finite descent type by Harpaz--Wittenberg. |
| title | Non-abelian descent types |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2401.00340 |