English

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 kk, 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 kk-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