#### Identifier

etd-07082013-142038

#### Degree

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### Document Type

Dissertation

#### 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 G_{j} on infinitesimal neighborhoods X_{j} so that Ker(G_{1} &rarr G_{0})= TG_{0}, Here TG_{0} should be the Cousin resolution of TK_{m}(O_{X}) and X is any n-dimensional smooth projective variety over a field k, chark=0. Our main results are as follows. The existence of G_{j} 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.

#### Date

2013

#### Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

#### Recommended Citation

Yang, Sen, "Higher algebraic K-theory and tangent spaces to Chow groups" (2013). *LSU Doctoral Dissertations*. 2245.

https://digitalcommons.lsu.edu/gradschool_dissertations/2245

#### Committee Chair

Hoffman, Jerome