Galois cohomologies in p-adic Hodge theory

Abstract: Faltings computes Galois cohomologies of schemes over CDVR with semi-stable reduction, using his purity theorem. We do the calculation in the good reduction case in the local situation. Time permitting, we will explain how to use the result to get integral Hodge-Tate decompositions of etale cohomologies of modular curves, which are used to prove the triviality of geometric deformations of modular representations.