@inbook{10.2307/j.ctt130hk6f.11,
URL = {http://www.jstor.org/stable/j.ctt130hk6f.11},
abstract = {Suppose W is the Witt ring of a perfect field k of characteristic p, and X is a smooth k-scheme. The Frobenius automorphism of W is a PD morphism, covered by the absolute Frobenius endomorphism FXof X, and it follows that FXacts on the crystalline cohomology of X relative to W. In this chapter we shall study this action, in particular, its relationship to the Hodge filtration on crystalline cohomology (as determined from the ideal JX/S). The main global applications are Mazur's theorem (8.26), which says that (with suitable hypotheses on X) the action of Frobenius determines the},
bookauthor = {Pierre Berthelot and Arthur Ogus},
booktitle = {Notes on Crystalline Cohomology. (MN-21)},
pages = {8--1--8--50},
publisher = {Princeton University Press},
title = {Frobenius and the Hodge Filtration.},
year = {1978}
}