Speaker: Benjamin Schraen (CNRS)

Time: Every Monday , Wednesday and Friday From May 26th to June 6th, 11:00am-12:00am

Venue: Room 82J04, Jia Yi Bing Building, 82 Jing Chun Yuan, BICMR

Abstract: Using the notion of trianguline representation, we can construct a generalization of Kisin's finite slope space, originally constructed for modular forms. A conjecture of Hellmann predicts that eigenvarieties associated to unitary groups can be identified to unions of irreducible components of these finite slope spaces. The goal of the lectures will be to explain the proof of this conjecture in a wide range of cases, which is a joint work with C. Breuil and E. Hellmann. The main ingredients are patching arguments and locally analytic representations of p-adic Lie groups. We will detail consequences of this result, and explain why it gives new evidences for recent conjectures of Breuil on the locally analytic socle of the completed cohomology.

That will be 6 lectures:
1. Trianguline representations and finite slope space.
2. Automorphic forms and eigenvarieties.
3. Locally analytic representations.
4. Patching method.
5. Proof of the main result and arithmetic consequences.
6. Breuil's conjecture on the locally analytic socle in the p-adic correspondence.