Selmer Ranks of twists of hyperelliptic curves and superelliptic curves

2015/11/23 by Yu, Myungjun · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1511.07511

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.

Cited by

• Selmer ranks under quadratic twists satisfying the Heegner hypothesis
• Infinitely many genus two and three curves of small fixed positive rank

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