Joint IAS/PU Number Theory Seminar

Let p be a prime. I want to explain how to use the geometry of modular curves at infinite level and the Hodge–Tate period map to study regular de Rham p-adic Galois representations appearing in the p-adically completed cohomology of modular curves. We will show that these Galois representations up to twists come from modular forms, which was previously known by Emerton by totally different methods. One useful observation is to view modular curves at infinite level as a "correspondence" between classical modular curves and the flag variety.Let p be a prime. I want to explain how to use the geometry of modular curves at infinite level and the Hodge–Tate period map to study regular de Rham p-adic Galois representations appearing in the p-adically completed cohomology of modular curves. We will show that these Galois representations up to twists come from modular forms, which was previously known by Emerton by totally different methods. One useful observation is to view modular curves at infinite level as a "correspondence" between classical modular curves and the flag variety.