Iterating the algebraic etale-Brauer set

JOURNAL OF NUMBER THEORY

卷:182

Article

Balestrieri, F.¹ 

[1] Univ Oxford, Math Inst, Oxford OX2 6HD, England

关键词: Rational points;    Weak approximation;    Brauer-Manin obstruction;    Etale-Brauer obstruction;    Universal torsors;    Algebraic groups;   

DOI  :  10.1016/j.jnt.2017.05.027

来源: Elsevier

【 摘 要 】

In this paper, we iterate the algebraic etale-Brauer set for any nice variety X over a number field k with pi(et)(1)((X) over bar) finite and we show that the iterated set coincides with the original algebraic etale-Brauer set. This provides some evidence towards the conjectures by Colliot-Thelene on the arithmetic of rational points on nice geometrically rationally connected varieties over k and by Skorobogatov on the arithmetic of rational points on K3 surfaces over k; moreover, it gives a partial answer to an algebraic analogue of a question by Poonen about iterating the descent set. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free