Higher algebraic K-theory and tangent spaces to Chow groups

Abstract

In this work, using higher algebraic K-theory, we provide an answer to the following question asked by Green-Griffiths in [13]: Can one define the Bloch-Gersten-Quillen sequence Gj on infinitesimal neighborhoods Xj so that Ker(G1 &rarr G0)= TG0, Here TG0 should be the Cousin resolution of TKm(OX) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of Gj is discussed in chapter 3, following [8] and [18]. The main theorems are theorem5.2.5, theorem 5.2.6 and theorem 5.2.8. The proof for the above theorems, given in chapter 5, requires non-trivial techniques from higher algebraic K-theory and negative cyclic homology. The main ingredients of the proof are: existence of Chern character at spectrum level, effacement theorem and Goodwillie-type and Cathelineau-type results.