Tori and surfaces violating a local-to-global principle for rationality
Year: 2024
Type: article
Abstract: 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.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.602
Author: Boris Kunyavskiĭ
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Israel Science Foundation
Award: G6611866667
OpenAlex ID: W4403184346