DEFORMATION OF K-THEORETIC CYCLES

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 [9] (page 186-190): (1) For each positive integer p satisfying 1 <= p <= 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.