Pontryagin duality for iwasawa modules and abelian varieties

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

doi:10.1090/tran/7016

Pontryagin duality for iwasawa modules and abelian varieties

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

School of Mathematics and Physics

Capital Normal University
National Taiwan University
Sophia University

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

4 Citations (Scopus)

Abstract

We prove a functional equation for two projective systems of finite abelian p-groups, {a_n} and {ab_n}, endowed with an action of ℤ^d_p such that a_n can be identified with the Pontryagin dual of b_n for all n. Let K be a global field. Let L be a ℤ^d_p-extension of K (d ≥ 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.

Original language	English
Pages (from-to)	1925-1958
Number of pages	34
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	3
DOIs	https://doi.org/10.1090/tran/7016
Publication status	Published - 2018

Keywords

Abelian variety
Iwasawa theory
Pontryagin duality
Selmer group

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10.1090/tran/7016

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@article{e69a3e8a4e0c42be9d947c3fea3d5523,

title = "Pontryagin duality for iwasawa modules and abelian varieties",

abstract = "We prove a functional equation for two projective systems of finite abelian p-groups, \{an\} and \{abn\}, endowed with an action of ℤdp such that an can be identified with the Pontryagin dual of bn for all n. Let K be a global field. Let L be a ℤdp-extension of K (d ≥ 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.",

keywords = "Abelian variety, Iwasawa theory, Pontryagin duality, Selmer group",

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

note = "Funding Information: Received by the editors February 4, 2016 and, in revised form, June 27, 2016. 2010 Mathematics Subject Classification. Primary 11S40; Secondary 11R23, 11R34, 11R42, 11R58, 11G05, 11G10. Key words and phrases. Pontryagin duality, abelian variety, Selmer group, Iwasawa theory. The first, second, and third authors were partially supported by the National Science Council of Taiwan, grants NSC98-2115-M-110-008-MY2, NSC100-2811-M-002-079, and NSC99-2115-M-002-002-MY3, respectively. The fourth author was supported by EPSRC. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2018",

doi = "10.1090/tran/7016",

language = "English",

volume = "370",

pages = "1925--1958",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

number = "3",

}

TY - JOUR

T1 - Pontryagin duality for iwasawa modules and abelian varieties

AU - Lai, King Fai

AU - Longhi, Ignazio

AU - Tan, Ki Seng

AU - Trihan, Fabien

N1 - Funding Information: Received by the editors February 4, 2016 and, in revised form, June 27, 2016. 2010 Mathematics Subject Classification. Primary 11S40; Secondary 11R23, 11R34, 11R42, 11R58, 11G05, 11G10. Key words and phrases. Pontryagin duality, abelian variety, Selmer group, Iwasawa theory. The first, second, and third authors were partially supported by the National Science Council of Taiwan, grants NSC98-2115-M-110-008-MY2, NSC100-2811-M-002-079, and NSC99-2115-M-002-002-MY3, respectively. The fourth author was supported by EPSRC. Publisher Copyright: © 2017 American Mathematical Society.

PY - 2018

Y1 - 2018

N2 - We prove a functional equation for two projective systems of finite abelian p-groups, {an} and {abn}, endowed with an action of ℤdp such that an can be identified with the Pontryagin dual of bn for all n. Let K be a global field. Let L be a ℤdp-extension of K (d ≥ 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.

AB - We prove a functional equation for two projective systems of finite abelian p-groups, {an} and {abn}, endowed with an action of ℤdp such that an can be identified with the Pontryagin dual of bn for all n. Let K be a global field. Let L be a ℤdp-extension of K (d ≥ 1), unramified outside a finite set of places. Let A be an abelian variety over K. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of A.

KW - Abelian variety

KW - Iwasawa theory

KW - Pontryagin duality

KW - Selmer group

UR - https://www.scopus.com/pages/publications/85039808744

U2 - 10.1090/tran/7016

DO - 10.1090/tran/7016

M3 - Article

AN - SCOPUS:85039808744

SN - 0002-9947

VL - 370

SP - 1925

EP - 1958

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 3

ER -

Pontryagin duality for iwasawa modules and abelian varieties

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Keywords

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