2-selmer near-companion curves

Myungjun Yu

doi:10.1090/tran/7563

2-selmer near-companion curves

Myungjun Yu

Department of Mathematics

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

1 Citation (Scopus)

Abstract

Let E and A be elliptic curves over a number field K. Let_χ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of E^χ and A^χ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].

Original language	English
Pages (from-to)	425-440
Number of pages	16
Journal	Transactions of the American Mathematical Society
Volume	372
Issue number	1
DOIs	https://doi.org/10.1090/tran/7563
Publication status	Published - 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/tran/7563

Cite this

@article{cd3e2e6a355a4dbda87ae2b76be0e2f1,

title = "2-selmer near-companion curves",

abstract = "Let E and A be elliptic curves over a number field K. Letχ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].",

author = "Myungjun Yu",

note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2019",

doi = "10.1090/tran/7563",

language = "English",

volume = "372",

pages = "425--440",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - 2-selmer near-companion curves

AU - Yu, Myungjun

PY - 2019

Y1 - 2019

N2 - Let E and A be elliptic curves over a number field K. Letχ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].

AB - Let E and A be elliptic curves over a number field K. Letχ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].

UR - http://www.scopus.com/inward/record.url?scp=85060639163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060639163&partnerID=8YFLogxK

U2 - 10.1090/tran/7563

DO - 10.1090/tran/7563

M3 - Article

AN - SCOPUS:85060639163

VL - 372

SP - 425

EP - 440

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -

2-selmer near-companion curves

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this