Pontryagin duality for iwasawa modules and abelian varieties

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1925-1958
Number of pages34
JournalTransactions of the American Mathematical Society
Issue number3
Publication statusPublished - 2018


  • Abelian variety
  • Iwasawa theory
  • Pontryagin duality
  • Selmer group


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