Chern classes and cycle classes in rigid cohomology. (Classes de Chern et classes de cycles en cohomologie rigide).(French)Zbl 1083.14505

Summary: We define in this article Chern classes and cycle classes in rigid cohomology. Then we prove that these constructions verify the expected properties. The rigid cohomology is a Weil cohomology.

MSC:

 14F30 $$p$$-adic cohomology, crystalline cohomology 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14G22 Rigid analytic geometry
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