Date of Award
Doctor of Philosophy (PhD)
There are two natural questions one can ask about the higher Chow group of number fields:
One is its torsion, the other one is its relation with the homology of GLn. For the first
question, based on some earlier work, the integral regulator on higher Chow complexes
introduced here can put a lot of earlier result on a firm ground. For the second question, we
give a counterexample to an earlier proof of the existence of linear representatives of higher
Chow groups of number fields.
Chapter 1 gives a general picture of the two problems we are talking about. Chapter 2
contains the background material on higher Chow groups. In chapter 3, we showed the full
process of proving the existence of integral regulator on higher Chow complexes, and give
the explicit expression for it, and some direct application. In chapter 4, we introduced the
conjecture of the (rational) surjectivity of the map from linear higher Chow group to the
simplicial higher Chow group, its earlier proof and the counter example. However, it is not a
global counter example, thus the original conjecture is still open.
Chair and Committee
Mohan Kumar, Roya Beheshti, John McCarthy, Adrian Clingher,
Li, Muxi, "Regulators on Higher Chow Groups" (2018). Arts & Sciences Electronic Theses and Dissertations. 1558.