Algebraic K-theory

Webel 98-01560建议研究代数K-理论、基元上同调和循环同调。他将通过从几何角度分析相关的基元上同调来研究代数K-场论的结构，并着眼于与其他K-理论的关系。他将使用亚当斯运算研究奇异变种的负K-理论的类似分解，并看看循环同调中存在多少K-理论的已知结构。最后，他将通过对有限维代数上的微分的约化来攻击Berger关于曲线的猜想。魏贝尔建议研究三种类型的不变量：代数K-理论，动机上同调和循环同调。它们既测量环和场等代数对象的性质，也测量像簇这样的几何对象的性质。最近的发展表明，这些不变量之间存在着很强的相互作用。魏贝尔将尝试使用几何方法，适合于基序上同调，和同调方法，适合于循环同调，来联系在这三个不变量中发现的结构。

Weibel98-01560Weibel proposes to do research in algebraic K-theory, motivic cohomology and cyclic homology. He will investigate the structure of the algebraic K-theory of fields by analyzing the associated motivic cohomology from a geometric perspective, with an eye to the relation with etale K-theory. He will study the analogous decomposition for the negative K-theory of singular varieties using Adams operations, and see how much of the known structure for K-theory is present in cyclic homology. Finally he will attack Berger's conjecture for curves by means of a reduction to differentials on finite-dimensional algebras.Weibel proposes to do research on three types of invariants: algebraic K-theory, motivic cohomology and cyclic homology. These measure properties of both algebraic objects like rings and fields, and geometric objects like varieties. Recent developments indicate that there is a strong interplay between these invariants. Weibel will attempt to use geometric methods, appropriate to motivic cohomology, and homological methods, appropriate to cyclic homology, to relate the structures found in these three invariants.