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On The Infinitesimal Theory Of Chow Groups, Benjamin F. Dribus
On The Infinitesimal Theory Of Chow Groups, Benjamin F. Dribus
LSU Doctoral Dissertations
The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure. Except for the case p=1, which yields an algebraic group, the Chow groups remain mysterious. This thesis explores a "linearization" approach to this problem, focusing on the infinitesimal structure of the Chow groups near their identity elements. This method was adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others. A famous formula of Bloch expresses the Chow …
Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang
Higher Algebraic K-Theory And Tangent Spaces To Chow Groups, Sen Yang
LSU Doctoral Dissertations
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 …