Rubin's conjecture on local units in the anticyclotomic tower at inert primes: $p=3$ case

Abstract

We prove Rubin's conjecture on the structure of local units in the anticyclotomic $\mathbb{Z}_p$-extension of unramified quadratic extension of $\mathbb{Q}_p$ in $p=3$ case by extending Burungale-Kobayashi-Ota's work.