Bass' $NK$群与$cdh$ -同调霍赫希尔德同调
Bass' $NK$ groups and $cdh$-fibrant Hochschild homology
摘要：
多项式环$R[t]$的$K$ -理论包含$R$的$K$ -理论作为被加数。对于$R$交换和包含$\Q$，我们描述$K_*(R[t])/K_*(R)$的霍赫希尔德同调和上同调的Kähler微分的$cdh$拓扑。我们用这个来回答Bass的问题，即$K_n(R)=K_n(R[t])$是否意味着$K_n(R)=K_n(R[t_1,t_2])$。答案是肯定的领域的无限超越度;配套文件arXiv：1004.3829提供了一个反例在数域。
英文摘要：
The $K$-theory of a polynomial ring $R[t]$ contains the $K$-theory of $R$ as a summand. For $R$ commutative and containing $\Q$, we describe $K_*(R[t])/K_*(R)$ in terms of Hochschild homology and the cohomology of Kähler differentials for the $cdh$ topology. We use this to address Bass' question, on whether $K_n(R)=K_n(R[t])$ implies $K_n(R)=K_n(R[t_1,t_2])$. The answer is positive over fields of infinite transcendence degree; the companion paper arXiv:1004.3829 provides a counterexample over a number field.
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