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

Alexei N. Skorobogatov, Yuri G. Zarhin

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)481-502
Number of pages22
JournalJournal of Algebraic Geometry
Volume17
Issue number3
DOIs
Publication statusPublished - 2008

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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