Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 10 (2003), No. 2, Page 391-419
Let XK 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 XK to the order of the Brauer group of a proper regular model of XK. We thereby partially answer a question of Grothendieck.