The p-adic Langlands Program and Breuil's Lattice Conjecture
Time: 2025-12-15
Published By: He Liu
Speaker(s): Hymn Chan (University of Toronto)
Time: 10:00-11:00 December 18, 2025
Venue: Room 77201, Jingchunyuan 78, BICMR
Roughly speaking, the p-adic Langlands correspondence is between n-dimensional p-adic Galois representations of GK and admissible unitary representations of GLn(K) over a p-adic Banach space, where K/Qp is a finite extension. This correspondence is known for the group GL2(Qp) , but remains unknown for GL2(K) for K/Qp unramified and non-trivial. Given a p-adic Galois representation of GK , one can construct an admissible unitary representation of GL2(K) using a global setup. However, it is unclear whether this construction is independent of the global setting. Breuil's lattice conjecture provides evidence for such a claim. Proving the conjecture demonstrates certain local-global compatibility. In the talk, I will explain the motivation behind the conjecture and briefly sketch the proof.
