Anglais
Bloch has defined higher Chow groups CHq(X,p) of a scheme X over a field k by constructing a complex out of the codimension q algebraic cycles on X×Ankn=0,1,2… We show that the Q-vector space CHq(X,p)Q k is naturally isomorphic to the weight q portion of the pth K-group of X,Kp(X)(q) for X a smooth quasi-projective variety over k, generalizing the ical isomorphism CHq(X)Q→K0(X)(q). We also show that the functors CHq(−,⋆)Q satisfy most of the properties of a Bloch-Ogus twisted duality theory. Finally, we show that the alternating cycle groups defined by Bloch agree with the rational higher Chow groups.
L'abonnement correspond aux 8 volumes annuels : 7 volumes d'Astérisque et le volume des exposés Bourbaki de l'année universitaire écoulée.
This subscription corresponds to 8 volumes: 7 volumes of Astérisque plus one volume with the texts of the Bourbaki talks given in the past year.