Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

The isomorphism between motivic cohomology and $K$-groups for equi-characteristic regular local rings

Pages: 281 – 285

DOI: https://dx.doi.org/10.4310/HHA.2012.v14.n1.a14


Yuki Kato (Mathematical Institute, Tohoku University, Aoba, Sendai, Japan)


One of the well-known problems in algebraic $K$-theory is the comparison of higher Chow groups and $K$-groups. In this paper, using the motivic complex defined by Voevodsky-Suslin-Friedlander, we prove the comparison theorem for equi-characteristic regular local rings.


algebraic cycles, higher Chow groups, algebraic $K$-theory

2010 Mathematics Subject Classification

14C25, 14F42, 19E15

Published 13 July 2012