Multiplicative reduction and the cyclotomic main conjecture for $\mathrm{GL}_2$

Christopher Skinner

Vol. 283 (2016), No. 1, 171–200

DOI: 10.2140/pjm.2016.283.171

Abstract

We show that the cyclotomic Iwasawa–Greenberg main conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In fact, the multiplicative case is deduced from the good case through the use of Hida families and a simple Fitting ideal argument.

Keywords

Iwasawa theory, special values of L-functions, Selmer groups

Mathematical Subject Classification 2010

Primary: 11G40, 11R23

Secondary: 11F67

Milestones

Received: 18 May 2014

Revised: 23 December 2014

Accepted: 31 December 2014

Published: 14 June 2016