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

Suslin教授将继续他对方案的Motivic上同调的研究，特别是它与代数K理论和域的Galois上同调的关系。在这个项目涉及的数学领域，许多数学家对各种事物如何相互联系做出了明智的猜测。苏斯林教授希望一劳永逸地证实其中一些猜测的真实性。他希望能够利用布洛赫和加藤的一个猜想与贝林森和利希滕鲍姆的另一个猜想之间的新发现的联系来洞察这两个猜想。这位研究人员还看到了将其他最新结果应用于弗里德兰德和米尔诺的著名猜想的机会。这个项目涉及代数、数论和几何的数学。在这些领域的现代方法中，一种强大的方法是从以相当简单的方式对事物进行分组开始。这个简单的分组被概括为更复杂但相关的重新分组。这一过程继续下去，建立了一个由越来越复杂的顺序分组组成的塔。这些塔楼的较高阶段通常完全无法管理。然而，数学家们已经学会了观察相互关联的整体，而不是个别部分。Motivic上同调、Galois上同调和代数K-理论是这种分组方法的三个明显不同的版本。然而，事实上，它们是密切相关的。关于两国关系的程度，人们有很多猜测或猜测，但确凿的事实更加难以捉摸。本项目致力于弄清这些事实。如果它成功了，结果将对数学的所有分支产生影响。

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.