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invariants birationnels

Journal of K-Theory (1)

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Invariants birationnels dans la suite spectrale de Bloch-Ogus
Alena Pirutka
Journal:

Journal of K-Theory / Volume 10 / Issue 3 / December 2012

Published online by Cambridge University Press:

07 June 2012, pp. 565-582

Print publication:

December 2012
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For a field k of cohomological dimension d we prove that the groups , (l, car.k) = 1, are birational invariants of smooth projective geometrically integral varieties over k of dimension n. Using the Kato conjecture, which has been recently established by Kerz and Saito [18], we obtain a similar result over a finite field for the groups . We relate one of these invariants with the cokernel of the l-adic cycle class map , which gives an analogue of a result of Colliot-Thélène and Voisin [5] 3.11 over ℂ for varieties over a finite field.