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

Myungjun Yu

doi:10.4310/MRL.2019.v26.n4.a12

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

Myungjun Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1217-1250
Number of pages	34
Journal	Mathematical Research Letters
Volume	26
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2019.v26.n4.a12
Publication status	Published - 2019

Bibliographical note

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

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.4310/MRL.2019.v26.n4.a12

Cite this

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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.",

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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