Potentially crystalline deformation rings and Serre weight conjectures: shapes and shadows

Daniel Le, Bao V. Le Hung, Brandon Levin, Stefano Morra

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We prove the weight part of Serre’s conjecture in generic situations for forms of U(3) which are compact at infinity and split at places dividing p as conjectured by Herzig (Duke Math J 149(1):37–116, 2009). We also prove automorphy lifting theorems in dimension three. The key input is an explicit description of tamely potentially crystalline deformation rings with Hodge–Tate weights (2, 1, 0) for K/ Qp unramified combined with patching techniques. Our results show that the (geometric) Breuil–Mézard conjectures hold for these deformation rings.

Original languageEnglish (US)
Pages (from-to)1-107
Number of pages107
JournalInventiones Mathematicae
Issue number1
StatePublished - Apr 1 2018


  • 11F33
  • 11F80

ASJC Scopus subject areas

  • General Mathematics

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