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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UR - http://www.scopus.com/inward/citedby.url?scp=0036872330&partnerID=8YFLogxK

U2 - 10.1016/S0012-9593(02)01109-6

DO - 10.1016/S0012-9593(02)01109-6

M3 - Article

AN - SCOPUS:0036872330

VL - 35

SP - 773

EP - 875

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

SN - 0012-9593

IS - 6

ER -