A Finiteness Theorem for the Brauer Group of Abelian Varieties and K3 Surfaces
نویسنده
چکیده
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.
منابع مشابه
A Finiteness Theorem for the Brauer Group of K3 Surfaces in Odd Characteristic
Let p be an odd prime and let k be a field finitely generated over the finite field with p elements. For any K3 surface X over k we prove that the the cokernel of the natural map Br(k) → Br(X) is finite modulo the p-primary torsion subgroup.
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