A principal homogeneous space (or torsor) $X$ of an abelian variety $A$ is a variety equipped with an $A$-action that is both free and transitive.
If $X$ has a rational point $O$ then we can view $X$ as an abelian variety with $O$ as its identity element by defining a group operation on $X$ in terms of the $A$-action on $O$.
Authors:
Knowl status:
- Review status: reviewed
- Last edited by Andrew Sutherland on 2016-03-29 23:11:30
Referred to by:
History:
(expand/hide all)
Not referenced anywhere at the moment.
- 2022-03-24 17:55:59 by Bjorn Poonen
- 2022-03-24 17:18:40 by Bjorn Poonen
- 2016-03-29 23:11:30 by Andrew Sutherland (Reviewed)