Characteristic ideals and Selmer groups

Andrea Bandini, Francesc Bars, Ignazio Longhi

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

© 2015 Elsevier Inc.. Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a ZpN-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p-primary Selmer group of A. To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Zpd-extension Fd/F and for any Zpd-1-extension contained in Fd, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Zp[[Gal(F/F)]] in the case A is a constant abelian variety.
Original languageEnglish
Pages (from-to)530-546
JournalJournal of Number Theory
Volume157
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • Characteristic ideals
  • Iwasawa theory
  • Selmer groups

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