Brauer groups and Tate-Shafarevich groups, by Cristian D. Gonzalez-Aviles

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.

Cristian D. Gonzalez-Aviles <>