BOUNDS FOR 2-SELMER RANKS IN TERMS OF SEMINARROW CLASS GROUPS

Hwajong Yoo; Myungjun Yu

doi:10.2140/pjm.2022.320.193

BOUNDS FOR 2-SELMER RANKS IN TERMS OF SEMINARROW CLASS GROUPS

Hwajong Yoo, Myungjun Yu

Department of Mathematics

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

1 Citation (Scopus)

Abstract

Let E be an elliptic curve over a number field K defined by a monic irreducible cubic polynomial F(x). When E is nice at all finite primes of K, we bound its 2-Selmer rank in terms of the 2-rank of a modified ideal class group of the field L = K[x]/(F(x)), which we call the seminarrow class group of L. We then provide several sufficient conditions for E being nice at a finite prime.

Original language	English
Pages (from-to)	193-222
Number of pages	30
Journal	Pacific Journal of Mathematics
Volume	320
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2022.320.193
Publication status	Published - 2022

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© 2022, Pacific Journal of Mathematics.All Rights Reserved.

All Science Journal Classification (ASJC) codes

General Mathematics

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10.2140/pjm.2022.320.193

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title = "BOUNDS FOR 2-SELMER RANKS IN TERMS OF SEMINARROW CLASS GROUPS",

abstract = "Let E be an elliptic curve over a number field K defined by a monic irreducible cubic polynomial F(x). When E is nice at all finite primes of K, we bound its 2-Selmer rank in terms of the 2-rank of a modified ideal class group of the field L = K[x]/(F(x)), which we call the seminarrow class group of L. We then provide several sufficient conditions for E being nice at a finite prime.",

keywords = "2-selmer rank, Elliptic curve, Ideal class group, Mordell–weil rank",

author = "Hwajong Yoo and Myungjun Yu",

year = "2022",

doi = "10.2140/pjm.2022.320.193",

language = "English",

volume = "320",

pages = "193--222",

journal = "Pacific Journal of Mathematics",

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AU - Yu, Myungjun

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N2 - Let E be an elliptic curve over a number field K defined by a monic irreducible cubic polynomial F(x). When E is nice at all finite primes of K, we bound its 2-Selmer rank in terms of the 2-rank of a modified ideal class group of the field L = K[x]/(F(x)), which we call the seminarrow class group of L. We then provide several sufficient conditions for E being nice at a finite prime.

AB - Let E be an elliptic curve over a number field K defined by a monic irreducible cubic polynomial F(x). When E is nice at all finite primes of K, we bound its 2-Selmer rank in terms of the 2-rank of a modified ideal class group of the field L = K[x]/(F(x)), which we call the seminarrow class group of L. We then provide several sufficient conditions for E being nice at a finite prime.

KW - 2-selmer rank

KW - Elliptic curve

KW - Ideal class group

KW - Mordell–weil rank

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SP - 193

EP - 222

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

BOUNDS FOR 2-SELMER RANKS IN TERMS OF SEMINARROW CLASS GROUPS

Abstract

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