The finiteness of the Tate–Shafarevich group over function fields for algebraic tori defined over the base field
Let $K$ be a field and $V$ be a set of rank one valuations of $K$. The corresponding Tate–Shafarevich group of a $K$-torus $T$ is $\Sha (T, V) = \ker (H^1(K, T) \rightarrow \prod _{v\,\in \,V} H^1(K_v, T))$. We prove that if $K = k(X)$ is the function field of a smooth geometrically integral quasi-p...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.588/ |
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