Asian Journal of Mathematics
Volume 23 (2019)
On extending Soulé’s variant of Bloch–Quillen identification
Pages: 49 – 70
Based on Balmer’s tensor triangular Chow group, we propose (Milnor) $K$-theoretic Chow groups of derived categories of schemes. These Milnor $K$-theoretic Chow groups recover the classical ones for smooth projective varieties and can detect nilpotent, while the classical ones can’t do.
As an application, we extend Soulé’s variant of Bloch–Quillen identification from smooth projective varieties to their trivial infinitesimal thickenings. This answers affirmatively a question by Green–Griffiths for trivial deformations.
Chow groups, deformation, $K$-theory, Bloch formula, Chern character, negative cyclic homology, derived category
2010 Mathematics Subject Classification
Received 25 April 2016
Received revised 14 July 2017
Published 3 May 2019