The spectral sequences relating algebraic K-theory to motivic cohomology

Eric M. Friedlander*, Andrei Suslin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)773-875
Number of pages103
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume35
Issue number6
DOIs
StatePublished - Nov 2002

ASJC Scopus subject areas

  • Mathematics(all)

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