关于循环同调的Hochschild-Kostant-Rosenberg定理
A Hochschild-Kostant-Rosenberg theorem for cyclic homology
摘要：
设$A$是域${\mathbb F}_2 = {\mathbb Z}/2$上的交换代数.证明了当$A$是光滑代数时，存在一个自然代数同态$\ell (A) \to HC^-_*(A)$，它是一个同构.因此，函子$\ell$可以看作是负循环同调的近似，而普通的循环同调$HC_*(A)$是自然的$\ell (A)$ -模。通常，存在光谱序列$E^2 = L_*(\ell )(A) \Rightarrow HC_*^- (A)$。我们对普通循环同调和周期循环同调找到了相应的逼近函子$\ell^+$和$\ell^{per}$，并建立了它们的谱序列.最后，我们讨论了近似的普适性。
英文摘要：
Let $A$ be a commutative algebra over the field ${\mathbb F}_2 = {\mathbb Z}/2$. We show that there is a natural algebra homomorphism $\ell (A) \to HC^-_*(A)$ which is an isomorphism when $A$ is a smooth algebra. Thus, the functor $\ell$ can be viewed as an approximation of negative cyclic homology and ordinary cyclic homology $HC_*(A)$ is a natural $\ell (A)$-module. In general, there is a spectral sequence $E^2 = L_*(\ell )(A) \Rightarrow HC_*^- (A)$. We find associated approximation functors $\ell^+$ and $\ell^{per}$ for ordinary cyclic homology and periodic cyclic homology, and set up their spectral sequences. Finally, we discuss universality of the approximations.
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