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

Andrei Suslin 98 01655教授Suslin将继续他的调查motivic上同调的计划，特别是它的关系与代数K-理论和伽罗瓦上同调的领域。 在这个项目涉及的数学领域，许多数学家已经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正确性。 他希望能够利用新发现的Bloch和Kato猜想与Beilinson和Lichtenbaum的另一个猜想之间的联系来深入了解它们。 调查人员还看到了机会，适用于其他最近的结果，著名的猜想弗里德兰德和米尔诺。这个项目涉及数学的边界代数，数论和几何。 现代研究这些领域的一个强有力的方法是以相当简单的方式对事物进行分组。 这个简单的分组被推广到更复杂但相关的重新分组。 这个过程继续下去，以建立一个越来越复杂的顺序分组的塔。 这些塔中的更高阶段通常是完全无法管理的。 然而，数学家们已经学会了观察相互关联的整体，而不是单个的部分。 动机上同调、伽罗瓦上同调和代数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。 关于这种关系的程度有很多猜测或猜测，但既定的事实更难以捉摸。 这个项目致力于确定这些事实。 如果成功，其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.