Multiplicative reduction and the cyclotomic main conjecture for gl2

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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.

Original languageEnglish (US)
Pages (from-to)171-200
Number of pages30
JournalPacific Journal of Mathematics
Volume283
Issue number1
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Iwasawa theory
  • Selmer groups
  • Special values of l-functions

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