Asian Journal of Mathematics
Volume 24 (2020)
Deformation of $K$-theoretic cycles
Pages: 303 – 330
For $X$ a $d$-dimensional smooth projective variety over a field $k$ of characteristic $0$, using higher algebraic $K$-theory, we study the following two questions asked by Mark Green and Phillip Griffiths in chapter 10 of  (page 186-190):
(1) For each positive integer $p$ satisfying $1 \leq p \leq d$, can one define the tangent space $TZ^p (X)$ to the cycle group $Z^p (X)$?
(2) Obstruction issues. The highlight is the appearance of negative $K$-groups which detect the obstructions to deforming cycles.
$K$-theory, algebraic cycles, deformation, tangent spaces, obstructions
2010 Mathematics Subject Classification
Received 5 February 2018
Accepted 29 May 2019
Published 8 September 2020