TY - JOUR
T1 - A finiteness theorem for the brauer group of Abelian varieties and KS surfaces
AU - Skorobogatov, Alexei N.
AU - Zarhin, Yuri G.
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
SN - 1056-3911
VL - 17
SP - 481
EP - 502
JO - Journal of Algebraic Geometry
JF - Journal of Algebraic Geometry
IS - 3
ER -