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.
|Original language||English (US)|
|Number of pages||103|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Nov 2002|
ASJC Scopus subject areas