Algebraic K-theory

weibel建议在代数k理论、动机上同调和循环同调方面进行研究。他将从几何的角度通过分析相关的动机上同调来研究代数场k理论的结构，并着眼于与代数场k理论的关系。他将利用Adams运算研究奇异变负k理论的类似分解，并观察k理论的已知结构中有多少存在于循环同调中。最后，他将通过还原有限维代数上的微分来攻击伯杰的曲线猜想。Weibel提出了三种不变量的研究：代数k理论、动机上同调和循环同调。它们既测量代数对象（如环和场）的性质，也测量几何对象（如变种）的性质。最近的发展表明，这些不变量之间有很强的相互作用。Weibel将尝试使用适合于动机上同调的几何方法和适合于循环同调的同调方法，将这三个不变量中的结构联系起来。

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.