Joint IAS/PU Arithmetic Geometry

The talk will be devoted to the problem of finiteness of the de Rham cohomology of holonomic D-modules, with the emphasis on the nonarchimedean setting. First, I will briefly recall what holonomic D-modules are and why they are important. Next, I will discuss known results about the finiteness of the de Rham cohomology of holonomic D-modules in various algebro-geometric settings. Finally, I will present my own results, which concern holonomic D-modules on smooth rigid-analytic varieties over the field C((t)) of formal Laurent series with complex coefficients.