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

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

Bibliographical note

Funding Information:
Yoo was supported by Research Resettlement Fund for the new faculty of Seoul National University. He was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1007169 and No. 2020R1A5A1016126). Yu was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01007604).

Publisher Copyright:
© 2022, Pacific Journal of Mathematics.All Rights Reserved.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.2140/pjm.2022.320.193

Cite this

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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.",

author = "Hwajong Yoo and Myungjun Yu",

note = "Funding Information: Yoo was supported by Research Resettlement Fund for the new faculty of Seoul National University. He was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1007169 and No. 2020R1A5A1016126). Yu was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01007604). Publisher Copyright: {\textcopyright} 2022, Pacific Journal of Mathematics.All Rights Reserved.",

year = "2022",

doi = "10.2140/pjm.2022.320.193",

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

Abstract

Bibliographical note

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