  The Chow groups of codimension-p algebraic cycles modulo rational equivalence
on a smooth algebraic variety X have steadfastly resisted the efforts of
algebraic geometers to fathom their structure. This book explores a
"linearization" approach to this problem, focusing on the infinitesimal
structure of the Chow groups near their identity elements. This method was
adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics
have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others.
A famous formula of Bloch expresses the Chow groups as Zariski sheaf cohomology
groups of algebraic K-theory sheaves on X. "Linearization" of the Chow groups
is thereby related to "linearization" of algebraic K-theory, which may be
described in terms of negative cyclic homology. The "proper formal
construction" arising from this approach is a "machine" involving the coniveau
spectral sequences arising from four different generalized cohomology theories
on X, with the last two sequences connected by the algebraic Chern character.
Due to the critical role of the coniveau filtration, I refer to this
construction as the coniveau machine. The main theorem in this book establishes
the existence of the coniveau machine for algebraic K-theory on a smooth
algebraic variety. An immediate corollary is a new formula expressing
generalized tangent groups of Chow groups in terms of negative cyclic homology.
