1 results
On the Notion of Visibility of Torsors
-
- Journal:
- Canadian Mathematical Bulletin / Volume 56 / Issue 2 / 01 June 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 225-228
- Print publication:
- 01 June 2013
-
- Article
-
- You have access
- Export citation
-
Let
$J$ be an abelian variety and 
$A$ be an abelian subvariety of $J$ , both defined over 
$Q$. Let 
$x$ be an element of 
${{H}^{1}}\left( Q,\,A \right)$. Then there are at least two definitions of $x$ being visible in $J$: one asks that the torsor corresponding to $x$ be isomorphic over $Q$ to a subvariety of $J$, and the other asks that $x$ be in the kernel of the natural map 
$
{{H}^{1}}\left( Q,\,A \right)\,\to \,{{H}^{1}}\left( \text{Q},\,J \right)$. In this article, we clarify the relation between the two definitions.
