Abstract

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.

Committee Chair

Matthew Kerr

Committee Members

Mohan Kumar, Roya Beheshti, John McCarthy, Adrian Clingher,

Comments

Permanent URL: https://doi.org/10.7936/K728071Z

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

Spring 5-15-2018

Language

English (en)

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Mathematics Commons

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