English

Brauer groups and Tate-Shafarevich groups

Algebraic Geometry 2007-05-23 v1 Number Theory

Abstract

Let X_K be a proper, smooth and geometrically connected curve over a global field K. In this paper we generalize a formula of Milne relating the order of the Tate-Shafarevich group of the Jacobian of X_K to the order of the Brauer group of a proper regular model of X_K. We thereby partially answer a question of Grothendieck.

Keywords

Cite

@article{arxiv.math/0104214,
  title  = {Brauer groups and Tate-Shafarevich groups},
  author = {Cristian D. Gonzalez-Aviles},
  journal= {arXiv preprint arXiv:math/0104214},
  year   = {2007}
}