Let X be a smooth scheme defined over a finite field k. We show that the rigid cohomology groups H_rig^i(X) are endowed with a weight filtration with respect to the Frobenius action. This is the crystalline analogue of the etale or classical theory. We apply the previous result to study the weight filtration on the crystalline realization of the mixed motive "(unipotent) fundamental group". We then study unipotent F-isocrystals endowed with weight filtration
Weights in Rigid Cohomology. Applications to Unipotent F-isocrystals.
CHIARELLOTTO, BRUNO
1998
Abstract
Let X be a smooth scheme defined over a finite field k. We show that the rigid cohomology groups H_rig^i(X) are endowed with a weight filtration with respect to the Frobenius action. This is the crystalline analogue of the etale or classical theory. We apply the previous result to study the weight filtration on the crystalline realization of the mixed motive "(unipotent) fundamental group". We then study unipotent F-isocrystals endowed with weight filtrationFile in questo prodotto:
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