Arithmetic D-modules and rigid cohomologies

Appears in collection : Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems

Currently, we have at least two cohomological formalisms for p-adic cohomologies : rigid co- homology and cohomology defined using arithmetic D-modules. It is natural to expect that these coincide, but this is not straightforward. One of the reasons is that the construction of the functor associating arithmetic D-modules to isocrystals, due to Caro, is very complicated. We give alter- native construction which enables us to compare the cohomology theory. This is a joint work with Chris Lazda.