Serre weights for locally reducible two-dimensional galois representations

Fred Diamond, David Savitt

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let F be a totally real field, and v a place of F dividing an odd prime p. We study the weight part of Serre's conjecture for continuous totally odd representations -ρ:GF →GL2-Fp) that are reducible locally at v. Let W be the set of predicted Serre weights for the semisimplification of -ρ|GFv}. We prove that, when |ρ|GFv} is generic, the Serre weights in W for which -ρ is modular are exactly the ones that are predicted (assuming that |ρ is modular). We also determine precisely which subsets of W arise as predicted weights when ρ|GFv} varies with fixed generic semisimplification.

Original languageEnglish (US)
Pages (from-to)639-672
Number of pages34
JournalJournal of the Institute of Mathematics of Jussieu
Volume14
Issue number3
DOIs
StatePublished - Jul 4 2015

Keywords

  • Breuil modules
  • Galois representations
  • Serre's conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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