Iwasawa Main Conjecture for Supersingular Elliptic Curves

Xin Wan

Published 2014-11-24Version 1

In this paper we prove the $\pm$-main conjecture formulated by Kobayashi for elliptic curves with good supersingular reduction at $p$ such that $a_p=0$, using a completely new idea of reducing it to another Iwasawa-Greenberg main conjecture which is more accessible. We also prove as a corollary the refined BSD formula in the supersingular case when the analytic rank is $0$. The argument uses in an essential way the recent study on explicit reciprocity law for Beilinson-Flach elements by Kings-Loeffler-Zerbes. (This work is in progress and hopefully will appear soon).