De Rham cohomology of rigid spaces

TL;DR

This paper introduces a new approach to defining de Rham cohomology for rigid spaces over non-archimedean fields, establishing key properties and relating it to existing rigid cohomology theories.

Contribution

It defines de Rham cohomology for rigid spaces using dagger spaces, proving functoriality, finiteness, and connecting it to Berthelot's rigid cohomology.

Findings

Established functorial properties of the cohomology groups.

Proved finiteness of the de Rham cohomology for rigid spaces.

Discussed the relation to Berthelot's rigid cohomology.

Abstract

We define de Rham cohomology groups for rigid spaces over non-archimedean fields of characteristic zero, based on the notion of dagger space. We establish some functorial properties and a finiteness result, and discuss the relation to the rigid cohomology as defined by P. Berthelot.