Automorphisms and symbols in K(,2)

"Much of the work in algebraic K-theory today is devoted to the search for ""motivic cohomology."" This hoped-for cohomology theory of algebraic geometry should be analogous to the known singular homology groups of topology. In this work we consider Goodwillie and Lichtenbaum's candidate for motivic cohomology. For R a regular ring, they define a ""weight"" filtration on the K-theory space K(R),$$K(R) = W\sp0 \gets W\sp1 \gets W\sp2 \gets \cdots,$$and then define the cohomology groups to be$H\sp{m}(X,\doubz (t)) = π\sb{2t-m}(W\sp{t}/W\sp{t+1}).$If what they propose is correct, then one would expect $\pi\sb{t}(W\sp{t}/W\sp{t+l})$ to be the weight t part of K(R). Here we present Goodwillie's proof that this is indeed the case when t = 2 and R is an algebraically closed field. We then continue his work by showing that $\pi\sb2(W\sp2/W\sp3)$ $\cong$ K$\sb2(R)$ for other fields, namely, we handle the cases, R = $\IR$, and R = $\doubc((T)).$ Our arguments also work when R is a finite field."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Holdener, Judy Ann

Contributors dc:contributor

• Evans, Graham

• Mathematics

Statement dc:rights

• Copyright 1994 Holdener, Judy Ann

Language dc:language

eng

Identifier

AAI9512397
(UMI)AAI9512397

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21180