Selmer Ranks of twists of hyperelliptic curves and superelliptic curves

Abstract

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.

arXiv comment30 pages, to appear in J. Number Theory

Cited by in corpus (1)

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