Geodesic
On the Notion of Visibility of Torsors
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 225-228

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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.
DOI : 10.4153/CMB-2011-182-0
Mots-clés : 11G35, 14G25, torsors, principal homogeneous spaces, visibility, Shafarevich-Tate group 
Agashe, Amod. On the Notion of Visibility of Torsors. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 225-228. doi: 10.4153/CMB-2011-182-0
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     year = {2013},
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     doi = {10.4153/CMB-2011-182-0},
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