Rubin's conjecture on local units in the anticyclotomic tower at inert primes

Ashay A. Burungale, Shinichi Kobayashi, Kazuto Ota

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We prove a fundamental conjecture of Rubin on the structure of local units in the anticyclotomic Zp-extension of the unramified quadratic extension of Qp for p ≥ 5 a prime. Rubin's conjecture underlies Iwasawa theory of the anticyclotomic deformation of a CM elliptic curve over the CM field at primes p of good super-singular reduction, notably the Iwasawa main conjecture in terms of the p-adic L-function. As a consequence, we prove an inequality in the p-adic Birch and Swinnerton-Dyer conjecture for Rubin's p-adic L-function.

Original languageEnglish
Pages (from-to)943-966
Number of pages24
JournalAnnals of Mathematics
Volume194
Issue number3
DOIs
Publication statusPublished - Nov 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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