Let p be a prime. I want to explain how to use the geometry of modular curves at infinite level and Hodge-Tate period map to study p-adic regular de Rham 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 and give a geometric description of the locally analytic representations of GL(2, Q_p) associated to them. These results were previously known by totally different methods.

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