Equivalence rationnelle, equivalence numerique et produits de courbes elliptiques sur un corps fini

Details Equivalence rationnelle, equivalence numerique et produits de courbes elliptiques sur un corps fini Equivalence rationnelle, equivalence numerique et produits de courbes elliptiques sur un corps fini

2002-05-14

arxiv.org/abs/math/0205158v2

Ann. Sci. Ec. Norm. Sup. 36 (2003), 977--2002

Mathematics

Algebraic Geometry

46 pages

Scientific paper

This is an update of the first version. We clarify that the main results apply to more general smooth projective varieties X than products of elliptic curves (briefly: X is of "abelian type", e.g. an abelian variety or a product of curves, and the Tate conjecture holds). We also deduce the Gersten conjecture for dvrs whose residue field is the function field of such an X. In an appendix, we construct some functoriality for etale motivic cohomology. Finally, some errors which were in Section 5 of the first version are corrected.

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