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On the Notion of Visibility of Torsors

Published online by Cambridge University Press:  20 November 2018

Amod Agashe
Amod Agashe*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL, U.S.A. e-mail: agashe@math.fsu.edu
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Abstract

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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.

Keywords

11G3514G25torsorsprincipal homogeneous spacesvisibilityShafarevich-Tate group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 2 , 01 June 2013 , pp. 225 - 228
Copyright
Copyright © Canadian Mathematical Society 2013

References

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