SMF

Bloch's higher Chow groups revisited

Bloch's higher Chow groups revisited

Marc LEVINE
     
                
  • Année : 1994
  • Tome : 226
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Pages : 235-320
  • DOI : 10.24033/ast.280

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)QK0(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.



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