Brauer groups and Tate-Shafarevich groups

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.

References in corpus (1)

• The Cassels-Tate pairing on polarized abelian varieties

Cited by in corpus (6)

• The conjectures of Artin-Tate and Birch-Swinnerton-Dyer
• Period and index of genus one curves over number fields
• Groups of components of Néron models of Jacobians and Brauer groups
• Arithmetic duality theorems for 1-motives over function fields
• A generalization of the Cassels-Tate dual exact sequence
• $\mathcal{D}$-elliptic sheaves and odd Jacobians