Alberto Vezzani (Universitá degli Studi di Milano)

Abstract: By drawing parallels to classical work by Monsky-Washnitzer, Elkik, Arabia and others, we motivate the study of (non-archimedean) motivic homotopy theory by showing that it can be used to define/re-define rational p-adic cohomology theories and prove new results about them. For example, we show how to define relative rigid cohomology and deduce finiteness properties for it (joint work with V. Ertl), solving a version of a conjecture by Berthelot for coefficients of geometric origin.