Brauer-Manin obstructions for homogeneous spaces of commutative affine algebraic groups over global fields

Autor:	Đonlagić, Azur
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 14G12 20G30 (primary) 11G35 14G17 20G10 (secondary)
Druh dokumentu:	Working Paper
Popis:	Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and of Colliot-Th\'el\`ene. In this article, we prove the analogous statements (and include obstructions to strong approximation over finite places) in the general case of a commutative affine group scheme $G$ of finite type over a global field in any characteristic. We also study finiteness of different variants of the second Tate-Shafarevich kernel (such as $S$-kernels and $\omega$-kernels) of the Cartier dual of $G$. All this is made possible by some recent theoretical advancements in positive characteristic, namely the finiteness theorems of B. Conrad and the generalized Tate duality of Z. Rosengarten. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.12127 Zobrazit plný text záznamu View this record from Arxiv