The distribution of Selmer ranks of quadratic twists of Jacobians of hyperelliptic curves

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Abstract

Let C be an odd degree hyperelliptic curve over a number field K and J be its Jacobian. Let JX be the quadratic twist of J by a quadratic character 2 Hom(GK; f1g). For every non-negative integer r, we show the probability that dimF2(Sel2(J=K)) = r for a certain family of quadratic twists can be given explicitly conditional on some heuristic hypothesis.

Original languageEnglish
Pages (from-to)1217-1250
Number of pages34
JournalMathematical Research Letters
Volume26
Issue number4
DOIs
Publication statusPublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 International Press of Boston, Inc.. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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