An example of non-cotorsion Selmer group

King Fai Lai; Ignazio Longhi; Ki Seng Tan; Fabien Trihan

doi:10.1090/S0002-9939-2015-12459-8

An example of non-cotorsion Selmer group

King Fai Lai, Ignazio Longhi, Ki Seng Tan, Fabien Trihan

School of Mathematics and Physics

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

1 Citation (Scopus)

Abstract

Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.

Original language	English
Pages (from-to)	2355-2364
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2015-12459-8
Publication status	Published - 2015

Keywords

Abelian variety
Frobenius
Iwasawa theory
Selmer group
Stickelberger element
Syntomic

Access to Document

10.1090/S0002-9939-2015-12459-8

Cite this

@article{21cf918ac38147e89822d96dd38d97bc,

title = "An example of non-cotorsion Selmer group",

abstract = "Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.",

keywords = "Abelian variety, Frobenius, Iwasawa theory, Selmer group, Stickelberger element, Syntomic",

author = "Lai, {King Fai} and Ignazio Longhi and Tan, {Ki Seng} and Fabien Trihan",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2015",

doi = "10.1090/S0002-9939-2015-12459-8",

language = "English",

volume = "143",

pages = "2355--2364",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "6",

}

TY - JOUR

T1 - An example of non-cotorsion Selmer group

AU - Lai, King Fai

AU - Longhi, Ignazio

AU - Tan, Ki Seng

AU - Trihan, Fabien

PY - 2015

Y1 - 2015

N2 - Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.

AB - Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.

KW - Abelian variety

KW - Frobenius

KW - Iwasawa theory

KW - Selmer group

KW - Stickelberger element

KW - Syntomic

UR - http://www.scopus.com/inward/record.url?scp=84925762437&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2015-12459-8

DO - 10.1090/S0002-9939-2015-12459-8

M3 - Article

AN - SCOPUS:84925762437

SN - 0002-9939

VL - 143

SP - 2355

EP - 2364

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -

An example of non-cotorsion Selmer group

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this