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arXiv · 1712.06249

Comparing the Brauer group and the Tate Shafarevich group

Thomas Geisser
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Abstract

We give a formula relating the order of the Brauer group of a surface fibered over a curve over a finite field to the order of the Tate-Shafarevich group of the Jacobian of the generic fiber. The formula implies that the Brauer group of a smooth and proper surface over a finite field is a square if it is finite.

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Thomas Geisser. 2017-12-18. Comparing the Brauer group and the Tate Shafarevich group. https://arxiv.org/abs/1712.06249

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