### Techniques of localization in the theory of algebraic cycles, by Marc Levine

We extend the technique used by Bloch in proving the localization property
for cycle complexes to give similar results for simplicial spaces. As an
application, we extend the localization property for Bloch's cycle complexes
to mixed characteristic. We also apply the machinery to the G-theory niveau
tower for the cosimplicial scheme X x Delta, proving a localization property
for the terms in the tower. Combined with the fundamental reinterpretation of
the Bloch-Lichtenbaum spectral sequence due to Friedlander and Suslin, this
allows one to extend the Bloch-Lichtenbaum spectral sequence to a spectral
sequence from motivic Borel-Moore homology to G-theory, for a scheme which is
essentially of finite type over a regular base scheme of dimension at most
one, including mixed characteristic. For a regular scheme, this gives a
spectral sequence from motivic cohomology (defined in terms of Bloch's higher
Chow groups) to K-theory.

Marc Levine <marc@neu.edu>