We study the variation of Selmer ranks of Jacobians of twists of hyperelliptic curves and superelliptic curves. We find sufficient conditions for such curves to have infinitely many twists whose Jacobians have Selmer ranks equal to r, for any given nonnegative integer r. This generalizes earlier results of Mazur-Rubin on elliptic curves.
|Number of pages||38|
|Journal||Journal of Number Theory|
|Publication status||Published - 2016 Mar 1|
Bibliographical noteFunding Information:
This material is based upon work supported by the National Science Foundation under grant DMS-1065904 .
© 2015 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory