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Brauer groups and Tate-Shafarevich groups

Cristian D. Gonzalez-Aviles
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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.

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Cristian D. Gonzalez-Aviles. 2001-04-24. Brauer groups and Tate-Shafarevich groups. https://arxiv.org/abs/math/0104214

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