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- W2783287425 abstract "Let $mathcal X$ be a regular variety, flat and proper over a complete regular curve over a finite field, such that the generic fiber $X$ is smooth and geometrically connected. We prove that the Brauer group of $mathcal X$ is finite if and only Tate's conjecture for divisors on $X$ holds and the Tate-Shafarevich group of the Albanese variety of $X$ is finite, generalizing a theorem of Artin and Grothendieck for surfaces to arbitrary relative dimension. We also give a formula relating the orders of the group under the assumption that they are finite, generalizing the formula given for a surface." @default.
- W2783287425 created "2018-01-26" @default.
- W2783287425 creator A5035321624 @default.
- W2783287425 date "2018-01-08" @default.
- W2783287425 modified "2023-09-27" @default.
- W2783287425 title "Tate's conjecture and the Tate-Shafarevich group over global function fields" @default.
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