A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces
By Alexei N. Skorobogatov, Yuri G. Zarhin. 2006
98 citations recorded by the source corpus.
Let k be a field finitely generated over the field of rational numbers, and Br(k) the Brauer group of k. For an algebraic variety X over k we consider the cohomological Brauer–Grothendieck group Br(X). We prove that the quotient of Br(X) by the image of Br(k) is finite if X is a K3 surface. When X is an abelian variety over k, and X is the variety over an algebraic closure k of k obtained from X by the extension of the ground field, we prove that the image of Br(X) in Br(X) is finite.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/505c10e7292fe587b5770c9a881513faca0370b8
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Citations in the corpus
- Transcendental obstructions to weak approximation on general K3 surfaces (2010, background): “(2) It would be interesting to figure out ifX(Q) = X(Q) (see the introduction of [SZ08]).”
- Lectures on K3 Surfaces (2016, background): “However, up to Br(k) certain general finiteness results for K3 surfaces in characteristic zero have been proved by Skorobogatov and Zarhin in [570].”