2023/05/05 by Boris Kunyavskiı̆, Kunyavskii, Boris
Computer Science · Mathematics · #14E08 14G12 14G25 14J20 14J26 14M20 11G35 20G30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2305.03481
openalex publication_date 2023/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.