Brauer groups and Tate-Shafarevich groups

Details Brauer groups and Tate-Shafarevich groups Brauer groups and Tate-Shafarevich groups

2001-04-24

arxiv.org/abs/math/0104214v1

Mathematics

Algebraic Geometry

Scientific paper

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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