Algebraic K-theory, Motivic Cohomology and Homology of Linear Groups

点击翻译按钮获取中文摘要

Andrei Suslin98 01655Professor Suslin will continue his investigation of the motivic cohomology of schemes, in particular its relationship with algebraic K-theory and with the Galois cohomology of fields. In the area of mathematics this projects deals, many mathematicians have made informed guesses about how various things interconnect. Professor Suslin hopes to establish the validity of some of these guesses once and for all. He expects to be able to capitalize on the newly discovered connection between a conjecture of Bloch and Kato and another conjecture of Beilinson and Lichtenbaum to gain insight about them both. The investigator also sees the opportunity to apply other recent results to the famous conjecture of Friedlander and Milnor.This project involves mathematics on the borderlines of Algebra, Number Theory and Geometry. A powerful method in the modern approach to these fields begins by grouping things in rather simple ways. This simple grouping is generalized to a more complicated but related regrouping. This process is continued to build a tower of more and more complicated sequential groupings. The higher stages in these towers are usually completely unmanageable. Mathematicians have learned, however, to look at the interconnected whole rather than the individual parts. Motivic cohomology, Galois cohomology, and algebraic K-theory are three apparently different versions of this method of grouping. In fact, however, they are intimately related. There are a lot of guesses or conjectures about the extent of the relations, but established facts are more elusive. This project is devoted to the nailing down these facts. If it succeeds, the results will have impact in all branches of mathematics.