Published June 2017
| Submitted
Journal Article
Open
On Selmer Rank Parity of Twists
- Creators
- Hadian, Majid
- Weidner, Matthew
Abstract
In this paper we study the variation of the p-Selmer rank parities of p-twists of a principally polarized Abelian variety over an arbitrary number field K and show, under certain assumptions, that this parity is periodic with an explicit period. Our result applies in particular to principally polarized Abelian varieties with full K-rational p-torsion subgroup, arbitrary elliptic curves, and Jacobians of hyperelliptic curves. Assuming the Shafarevich–Tate conjecture, our result allows one to classify the rank parities of all quadratic twists of an elliptic or hyperelliptic curve after a finite calculation.
Additional Information
© 2016 Australian Mathematical Publishing Association Inc. Published online: 28 September 2016. The second author would like to thank the Caltech Student-Faculty Programs office for supporting his research on this project through a Summer Undergraduate Research Fellowship.Attached Files
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Additional details
- Eprint ID
- 78027
- Resolver ID
- CaltechAUTHORS:20170608-090925361
- Caltech Summer Undergraduate Research Fellowship (SURF)
- Created
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2017-06-08Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field