Sous-groupe de Brauer invariant et obstruction de descente itérée

authored by

Yang Cao

Abstract

For a quasi-projective smooth geometrically integral variety over a number field k, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an open question of Poonen. Our main tools are the notion of invariant Brauer subgroup and the notion of invariant étale Brauer–Manin obstruction for a k-variety equipped with an action of a connected linear algebraic group.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Algebra and Number Theory

Volume

14

Pages

2151-2183

No. of pages

33

ISSN

1937-0652

Publication date

18.09.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.48550/arXiv.1704.05425 (Access: Open)
https://doi.org/10.2140/ant.2020.14.2151 (Access: Closed)