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COMPARING THE BRAUER GROUP TO THE TATE–SHAFAREVICH GROUP
Published online by Cambridge University Press: 19 July 2018
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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- © Cambridge University Press 2018
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