@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",

}