THE FONTAINE-MAZUR CONJECTURE IN THE RESIDUALLY REDUCIBLE CASE

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Abstract

We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper.

Original languageEnglish (US)
Pages (from-to)1031-1169
Number of pages139
JournalJournal of the American Mathematical Society
Volume35
Issue number4
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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