On the Notion of Visibility of Torsors

Canadian mathematical bulletin

Amod Agashe¹ 

[1] Department of Mathematics, Florida State University, Tallahassee, FL, U.S.A.

关键词: torsors;    principal homogeneous spaces;    visibility;    Shafarevich-Tate group;   

DOI  :  10.4153/CMB-2011-182-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $J$ be an abelian variety and$A$ be an abelian subvariety of $J$, both defined over $mathbf{Q}$.Let $x$ be an element of $H^1(mathbf{Q},A)$. Then there are at least two definitions of $x$ being visible in $J$:one asks that the torsor corresponding to $x$ be isomorphic over $mathbf{Q}$to a subvariety of $J$, and the other asks that $x$ be in the kernelof the natural map $H^1(mathbf{Q},A) o H^1(mathbf{Q},J)$. In this article, weclarify the relation between the two definitions.

【 授权许可】

Unknown