WEIGHTS IN RIGID COHOMOLOGY - APPLICATIONS TO UNIPOTENT F-ISOCRYSTALS

Let X be a smooth scheme defined over a finite field k. We show that t he rigid cohomology groups H-rig(.)(X) are endowed with a weight filtr ation with respect to the Frobenius action. This is the crystalline an alogue of the etale or classical theory. We apply the previous result to study the weight filtration on the crystalline realization of the m ixed motive ''(unipotent) fundamental group''. We then study unipotent F-isocrystals endowed with weight filtration. (C) Elsevier, Paris.