Potentially crystalline deformation rings in the ordinary case

Brandon Levin, Stefano Morra

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study potentially crystalline deformation rings for a residual, ordinary Galois representation £: GQp → GL3(Fp).We consider deformations with Hodge-Tate weights (0, 1, 2) and inertial type chosen to contain exactly one Fontaine-Laffaille modular weight for £. We show that, in this setting, the potentially crystalline deformation space is formally smooth over Zp and any potentially crystalline lift is ordinary. The proof requires an understanding of the condition imposed by the monodromy operator on Breuil modules with descent datum, in particular, that this locus mod p is formally smooth.

Original languageEnglish (US)
Pages (from-to)1923-1964
Number of pages42
JournalAnnales de l'Institut Fourier
Issue number5
StatePublished - 2016
Externally publishedYes


  • Integral padic Hodge theory
  • Potentially crystalline deformation rings
  • Serre-type conjectures

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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