Abstract
In 1960s, Grothendieck introduced the notion of infinitesimal cohomology for a complex algebraic variety, recomputing its algebraic de Rham cohomology using infinitesimal thickenings. He also proposed the analogous notion in characteristic p, namely crystalline cohomology, which was developed later by Berthelot. Motivated by the ideas, in this talk we consider their p-adic analytic analogue, introducing the crystalline cohomology over a rigid analytic space. We will see that this cohomology theory enjoys various properties as in the algebraic case. Moreover, we will compare this crystalline cohomology with other cohomology theories for rigid analytic spaces.
