Asian Journal of Mathematics

Volume 23 (2019)

Number 1

On extending Soulé’s variant of Bloch–Quillen identification

Pages: 49 – 70

DOI: https://dx.doi.org/10.4310/AJM.2019.v23.n1.a4

Author

Sen Yang (School of Mathematics, Southeast University, Nanjing, Jiangsu, China; and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Abstract

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.

Keywords

Chow groups, deformation, $K$-theory, Bloch formula, Chern character, negative cyclic homology, derived category

2010 Mathematics Subject Classification

14C25

Full Text (PDF format)

Received 25 April 2016

Received revised 14 July 2017

Published 3 May 2019