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Finiteness of cohomology of arithmetic families of $(\varphi, \Gamma)$-modules
We will explain constructions of Robba rings and $(\\varphi, \\Gamma)$-modules of p-adic Hodge theory. We will describe new proofs of some results on finiteness of cohomology of these modules, and indicate their applications to the theory of $p$-adic families of automorphic forms. This is part of ongoing work with Eugen Hellmann and Ruochuan Liu.