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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.

For a central simple k-algebra A with indk (A) ∈ k×, Suslin defined a cohomological invariant for SK1 (A) [Sus2]. In this text, we generalise his invariant to any central simple k-algebra using a lift from positive characteristic to characteristic 0. To be able to define the invariant, we use Kato's cohomology of logarithmic differentials [Kat1].

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Invariants birationnels dans la suite spectrale de Bloch-Ogus

L'invariant de Suslin en caractéristique positive

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2 results

Invariants birationnels dans la suite spectrale de Bloch-Ogus

L'invariant de Suslin en caractéristique positive