A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation

Yisheng Tian

doi:10.5802/crmath.547

Research article - Algebraic geometry, Number theory

A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation

Yisheng Tian ¹

¹ Institute for Advanced Study in Mathematics, Harbin Institute of Technology, 150001 Harbin, China

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 257-264.

Abstract

We show that certain Tate–Shafarevich groups are unramified which enables us to give an obstruction to the Hasse principle for torsors under tori over $p$ -adic function fields.

Received: 2021-01-23
Revised: 2021-12-30
Accepted: 2023-07-21
Published online: 2024-05-02

DOI: 10.5802/crmath.547

Author's affiliations:

Yisheng Tian ¹

¹ Institute for Advanced Study in Mathematics, Harbin Institute of Technology, 150001 Harbin, China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {A {Comparison} of {Cohomological} {Obstructions} to the {Hasse} {Principle} and to {Weak} {Approximation}},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2024},
     doi = {10.5802/crmath.547},
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Yisheng Tian. A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 257-264. doi : 10.5802/crmath.547. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.547/

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