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On standard norm varieties

Nikita A. KarpenkoAlexander S. Merkurjev — 2013

Annales scientifiques de l'École Normale Supérieure

Let  p be a prime integer and F a field of characteristic 0 . Let  X be theof a symbol in the Galois cohomology group H n + 1 ( F , μ p n ) (for some n 1 ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field F ( X ) has the following property: for any equidimensional variety Y , the change of field homomorphism CH ( Y ) CH ( Y F ( X ) ) of Chow groups with coefficients in integers localized at  p is surjective in codimensions < ( dim X ) / ( p - 1 ) . One of the main ingredients of the proof is a computation of...

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