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

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.

Cited by in corpus (3)

• Pariah moonshine
• Main conjectures for non-CM elliptic curves at good ordinary primes
• Arithmetic of critical $p$-adic $L$-functions