Sous-groupe de Brauer invariant et obstruction de descente it\'er\'ee
Algebraic Geometry
2020-09-23 v5
Abstract
For a quasi-projective smooth geometrically integral variety over a number field , 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. The key idea is the notion of invariant Brauer subgroup and the notion of invariant \'etale Brauer-Manin obstruction for a -variety equipped with an action of a connected linear algebraic group.
Keywords
Cite
@article{arxiv.1704.05425,
title = {Sous-groupe de Brauer invariant et obstruction de descente it\'er\'ee},
author = {Yang Cao},
journal= {arXiv preprint arXiv:1704.05425},
year = {2020}
}
Comments
in French, 30 pages