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Motivic Complexes of Suslin and Voevodsky

Motivic Complexes of Suslin and Voevodsky

Eric M. FRIEDLANDER
Motivic Complexes of Suslin and Voevodsky
  • Année : 1997
  • Tome : 245
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Class. Math. : 19E15, 19F99
  • Pages : 355-378
  • DOI : 10.24033/ast.399

Following work of A. Beilinson, S. Bloch, S. Lichtenbaum and others, Andrei Suslin and Vladimir Voevodsky have established much of the desired formalism expected of motivic cohomology for varieties over a field. The motivic chain complexes $\mathbf {Z}(n)$ of sheaves with transfers are constructed using sheaves of equidimensional cycles proper of relative dimension 0. Techniques of Suslin-Voevodsky permit the proofs of many good properties as well as some fundamental computations. Of particular importance is the close relationship between algebraic $K$-theory and motivic cohomology, the cohomology of $\mathbf {Z}(n)$.

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