A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation
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.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.547/ |
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| _version_ | 1825206225581637632 |
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| author | Tian, Yisheng |
| author_facet | Tian, Yisheng |
| author_sort | Tian, Yisheng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-44b40940c4064cf78c1338f2f3a359a6 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-44b40940c4064cf78c1338f2f3a359a62025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G325726410.5802/crmath.54710.5802/crmath.547A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak ApproximationTian, Yisheng0Institute for Advanced Study in Mathematics, Harbin Institute of Technology, 150001 Harbin, ChinaWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.547/ |
| spellingShingle | Tian, Yisheng A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation Comptes Rendus. Mathématique |
| title | A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation |
| title_full | A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation |
| title_fullStr | A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation |
| title_full_unstemmed | A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation |
| title_short | A Comparison of Cohomological Obstructions to the Hasse Principle and to Weak Approximation |
| title_sort | comparison of cohomological obstructions to the hasse principle and to weak approximation |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.547/ |
| work_keys_str_mv | AT tianyisheng acomparisonofcohomologicalobstructionstothehasseprincipleandtoweakapproximation AT tianyisheng comparisonofcohomologicalobstructionstothehasseprincipleandtoweakapproximation |