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- W4320002216 abstract "Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak approximation problems for $K$-homogeneous spaces of $text{SL}_n$ with stabilizers extension of a group of multiplicative type by a unipotent group. The tools used are arithmetic (local and global) duality theorems in Galois cohomology, in combination with techniques similar to those used by Harari, Szamuely, Colliot-Th'el`ene, Sansuc, and Skorobogatov. In the case where the curve is defined over a higher-dimensional local field, coarser results are also given." @default.
- W4320002216 created "2023-02-11" @default.
- W4320002216 creator A5013082788 @default.
- W4320002216 date "2022-11-16" @default.
- W4320002216 modified "2023-09-28" @default.
- W4320002216 title "Arithmetics of homogeneous spaces over $p$-adic function fields" @default.
- W4320002216 doi "https://doi.org/10.48550/arxiv.2211.08986" @default.
- W4320002216 hasPublicationYear "2022" @default.
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