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The p-adic Langlands Program and Breuil's Lattice Conjecture
发布时间：2025年12月15日
浏览次数：1039
发布者: He Liu
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.
