Comparing the Brauer group and the Tate Shafarevich group

Published 18 Dec 2017 in math.AG and math.NT | (1712.06249v3)

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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Authors (1)

Thomas Geisser

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