Invariants birationnels dans la suite spectrale de Bloch-Ogus

Details Invariants birationnels dans la suite spectrale de Bloch-Ogus Invariants birationnels dans la suite spectrale de Bloch-Ogus

2011-06-15

arxiv.org/abs/1106.3001v1

Mathematics

Algebraic Geometry

Scientific paper

For a field k of cohomological dimension d we prove that some E_2-terms of the Bloch-Ogus spectral sequence are birational invariants of smooth projective geometrically integral varieties over k. Over a finite field, we relate one of these invariants with the cokernel of the l-adic cycle class map for 1-cycles. Soit k un corps de dimension cohomologique d. On \'etablit que certains E_2-termes de la suite spectrale de Bloch-Ogus sont des invariants birationnels des k-vari\'et\'es projectives et lisses, g\'eom\'etriquement int\`egres. Sur un corps fini, on relie un de ces invariants au conoyau de l'application classe de cycle l-adique \'etale pour les 1-cycles.

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