  The de Rham comparison theorem for varieties, first proved by Faltings, gives
the de Rham cohomology of a variety in terms of its p-adic etale cohomology. We
extend this theorem to proper, smooth Deligne-Mumford stacks. Two approaches
are given, which both in the end reduce the problem to the already known
comparison theorem for varieties. The first approach employs the formalism of
Weil cohomologies. Unfortunately, this does not result in a complete proof of
the comparison theorem, as the author was unable to prove the required
compatibility between intersections and cup products. Nevertheless, the author
thought the results that are obtained and the method that is suggested
interesting enough to include them. The second approach uses simplicial methods
and is based on versions of the comparison theorem by Kisin and Tsuji. The
latter approach does result in a complete proof of the extended comparison
theorem.
