Finiteness of de Rham cohomology in rigid analysis

@article{GrosseKlnne2002FinitenessOD,
  title={Finiteness of de Rham cohomology in rigid analysis},
  author={Elmar Grosse-Kl{\"o}nne},
  journal={arXiv: Algebraic Geometry},
  year={2002}
}
For a big class of smooth dagger spaces --- dagger spaces are 'rigid spaces with overconvergent structure sheaf' --- we prove finite dimensionality of de Rham cohomology. This is enough to obtain finiteness of Berthelot's rigid cohomology also in the non-smooth case. We need a careful study of de Rham cohomology in situations of semi-stable reduction.