A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces
| dc.creator | Skorobogatov, Alexei | |
| dc.creator | Zarhin, Yuri | |
| dc.date | 2006-05-13 | |
| dc.date | 2007-11-05 | |
| dc.date.accessioned | 2026-07-07T08:40:18Z | |
| dc.date.available | 2026-07-07T08:40:18Z | |
| dc.description | Let $k$ be a field that is finitely generated over the field of rational numbers and $Br(k)$ the Brauer group of $k$. Let $X$ be an absolutely irreducible smooth projective variety over $k$, let $Br(X)$ be the cohomological Brauer-Grothendieck group of $X$ and $Br_0(X)$ the image of $Br(k)$ in $Br(X)$. We write $Br_1(X)$ for the subgroup of elements in $Br(X)$ that become trivial after replacing $k$ by its algebraic closure. We prove that $Br(X)/Br_0(X)$ is finite if $X$ is a $K3$ surface. When $X$ is (a principal homogeneous space of) an abelian variety over $k$ then we prove that $Br(X)/Br_1(X)$ is finite. | |
| dc.description | 20 pages Final version; to appear in the Journal of Algebraic Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0605351 | |
| dc.identifier | http://arxiv.org/abs/math/0605351 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141336 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G35; 14G25 | |
| dc.title | A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces | |
| dc.type | text |