Abstract
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 language | English (US) |
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Pages (from-to) | 1-107 |
Number of pages | 107 |
Journal | Inventiones Mathematicae |
Volume | 212 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2018 |
Externally published | Yes |
Keywords
- 11F33
- 11F80
ASJC Scopus subject areas
- General Mathematics