TY - JOUR
T1 - The spectral sequences relating algebraic K-theory to motivic cohomology
AU - Friedlander, Eric M.
AU - Suslin, Andrei
PY - 2002/11
Y1 - 2002/11
N2 - Beginning with the Bloch-Lichtenbaum exact couple relating the motivic cohomology of a field F to the algebraic K-theory of F, the authors construct a spectral sequence for any smooth scheme X over F whose E2 term is the motivic cohomology of X and whose abutment is the Quillen K-theory of X. A multiplicative structure is exhibited on this spectral sequence. The spectral sequence is that associated to a tower of spectra determined by consideration of the filtration of coherent sheaves on X by codimension of support.
AB - Beginning with the Bloch-Lichtenbaum exact couple relating the motivic cohomology of a field F to the algebraic K-theory of F, the authors construct a spectral sequence for any smooth scheme X over F whose E2 term is the motivic cohomology of X and whose abutment is the Quillen K-theory of X. A multiplicative structure is exhibited on this spectral sequence. The spectral sequence is that associated to a tower of spectra determined by consideration of the filtration of coherent sheaves on X by codimension of support.
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U2 - 10.1016/S0012-9593(02)01109-6
DO - 10.1016/S0012-9593(02)01109-6
M3 - Article
AN - SCOPUS:0036872330
SN - 0012-9593
VL - 35
SP - 773
EP - 875
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
IS - 6
ER -