Approximation faible pour les 0-cycles sur un produit de variétés rationnellement connexes

2014/09/09 by Yongqi Liang, Liang, Yongqi
Computer Science · Engineering · Mathematics · #11G35 #14D10 #14G25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1409.2782

openalex publication_date 2014/09/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Consider weak approximation for 0-cycles on a smooth proper variety defined over a number field, it is conjectured to be controlled by its Brauer group. Let X be a Châtelet surface or a smooth compactification of a homogeneous space of a connected linear algebraic group with connected stabilizer. Let Y be a rationally connected variety. We prove that weak approximation for 0-cycles on the product X× Y is controlled by its Brauer group if it is the case for Y after every finite extension of the base field. We do not suppose the existence of 0-cycles of degree 1 neither on X nor on Y.

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