Algebraic K-theory

Weibel 98 - 01560 Weibel提出研究代数K-理论、动机上同调和循环同调。 他将研究结构的代数K理论的领域分析相关motivic上同调从几何的角度来看，着眼于与etale K理论的关系。 他将研究类似的分解为负K-理论的奇异品种使用亚当斯操作，并看到有多少已知的结构K-理论是目前在循环同源。最后，他将攻击伯杰猜想曲线的手段减少微分有限维代数。韦伯提出做研究的三种类型的不变量：代数K-理论，动机上同调和循环同源。 它们既测量代数对象（如环和域）的属性，也测量几何对象（如簇）的属性。 最近的事态发展表明，这些不变量之间有很强的相互作用。 韦贝尔将尝试使用几何方法，适当的动机上同调，和同调方法，适当的循环同源，涉及的结构中发现这三个不变量。

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.