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

2 Citations (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

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10.1090/S0002-9939-2015-12459-8

Cite this

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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",

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AU - Lai, King Fai

AU - Longhi, Ignazio

AU - Tan, Ki Seng

AU - Trihan, Fabien

PY - 2015

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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 - https://www.scopus.com/pages/publications/84925762437

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

M3 - Article

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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

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Keywords

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