Ben Heuer (Universität Frankfurt)

Classical Sen theory describes C_p-semilinear representations of Galois groups of p-adic fields in terms of linear algebra data called Sen modules. I will first explain how this theory can be reinterpreted geometrically in terms of v-vector bundles, creating a relation to the p-adic Simpson correspondence. I will then explain how one can use this to upgrade Sen’s Theorem to a comparison of moduli spaces of Galois representations and Sen modules: This explains known subtleties in classical Sen theory in a geometric fashion. Finally, I will describe how we can use this to study moduli spaces of (phi,Gamma)-modules. This is joint work-in-progress with Eugen Hellmann.