F-Isocrystals on Open Varieties Results and Conjectures.

(a) In this paper we want to present some results and conjectures about crystalline cohomology. In particular, we shall show that many results from ℓ-adic étale cohomology have analogues, like the Lefschetz trace-formula, unipotence of monodromy, and the theory of weights. Our results are a sequel to the paper [Fa2]. However, there are some differences between the approaches taken. First of all, in [Fa2] we are mainly concerned with ℤp-valued cohomology, and show at the end how results carry over to the ℚp-adic theory (which works under much more general circumstances, but gives weaker results as we neglect p-torsion). Also, in [Fa2] the results are fairly complete, that is we show pretty much the results one can hope for. Finally, we were mostly interested in the relation between crystalline cohomology and p-adic étale cohomology. [ABSTRACT FROM AUTHOR]