Milnor K理论的一个Goodwillie型定理
A Goodwillie-type Theorem for Milnor K-Theory
摘要：
Goodwillie关于相对代数K理论与相对循环同调之间的有理同构，以及循环同调的lambda分解，说明了代数K理论、循环同调和微分形式之间的密切关系。在本文中，我证明了一个Goodwillie型定理的相关Milnor $K$ -理论，工作在一个非常一般的类交换环，通过Van der Kallen的稳定性准则定义。Van der Kallen和Bloch的早期结果是特例。这个结果可能通过弱化一些可逆性假设而推广到de Rahm-Witt复形，但是所考虑的环类对于预期的应用已经足够一般了。本文的主要动机来自应用的无穷小理论的周群，首先指出布洛赫在20世纪70年代，并突出在最近的工作绿色和格里菲斯。相关结果和几何应用在最后一节进行了讨论。
英文摘要：
Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology, and differential forms. In this paper, I prove a Goodwillie-type theorem for relative Milnor $K$-theory, working over a very general class of commutative rings, defined via the stability criterion of Van der Kallen. Early results of Van der Kallen and Bloch are special cases. The result likely generalizes in terms of de Rahm-Witt complexes, by weakening some invertibility assumptions, but the class of rings considered is already more than sufficiently general for the intended applications. The main motivation for this paper arises from applications to the infinitesimal theory of Chow groups, first pointed out by Bloch in the 1970's, and prominent in recent work of Green and Griffiths. Related results and geometric applications are discussed in the final section.
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