Tori and surfaces violating a local-to-global principle for rationality

Autor:	Kunyavskii, Boris
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Mathematics - Group Theory Mathematics - Number Theory 14E08 14G12 14G25 14J20 14J26 14M20 11G35 20G30
Druh dokumentu:	Working Paper
Popis:	We show that even within a class of varieties where the Brauer--Manin obstruction is the only obstruction to the local-to-global principle for the existence of rational points (Hasse principle), this obstruction, even in a stronger, base change invariant form, may be insufficient for explaining counter-examples to the local-to-global principle for rationality. We exhibit examples of toric varieties and rational surfaces over an arbitrary global field k each of those, in the absence of the Brauer obstruction to rationality, is rational over all completions of k but is not k-rational. Comment: 9 pages; revised according to the referee's remarks; accepted to Comptes Rendus Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.03481 Zobrazit plný text záznamu View this record from Arxiv