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arXiv · 2401.00340

Non-abelian descent types

Nguyen Manh Linh
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Abstract

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-Th\'el\`ene--Sansuc, the extended types by Harari--Skorobogatov, and the finite descent type by Harpaz--Wittenberg.

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Nguyen Manh Linh. 2023-12-30. Non-abelian descent types. https://doi.org/10.1016/j.jalgebra.2024.07.049

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