TY - JOUR

T1 - A finiteness theorem for the brauer group of Abelian varieties and KS surfaces

AU - Skorobogatov, Alexei N.

AU - Zarhin, Yuri G.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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U2 - 10.1090/S1056-3911-07-00471-7

DO - 10.1090/S1056-3911-07-00471-7

M3 - Article

AN - SCOPUS:66249124842

VL - 17

SP - 481

EP - 502

JO - Journal of Algebraic Geometry

JF - Journal of Algebraic Geometry

SN - 1056-3911

IS - 3

ER -