论文标题
在代数和平滑设置中的Hochschild同源性的比较
A comparison of Hochschild homology in algebraic and smooth settings
论文作者
论文摘要
考虑一个复杂的仿射品种$ \ tilde v $和$ \ tilde v $的真实分析Zariski强度submanifold V。我们将$ \ tilde v $上的常规功能的环$ O（\ tilde V）与戒指上的模块进行比较。 在切线空间的温和条件下，我们证明$ c^\ infty（v）$是$ o（\ tilde v）$的模块。由此，我们推断出有限类型代数的Hochschild同源性的比较定理，超过$ o（\ tilde v）$和$ c^\ infty（v）$的类似代数的Hochschild同源性。 我们还建立了这些结果的版本，用于在有限组G的作用下不变的$ \ tilde v $（v $ v $）。作为辅助结果，我们表明$ c^\ infty（v）$在$ c^\ infty（v）^g $上具有有限的模块。
Consider a complex affine variety $\tilde V$ and a real analytic Zariski-dense submanifold V of $\tilde V$. We compare modules over the ring $O (\tilde V)$ of regular functions on $\tilde V$ with modules over the ring $C^\infty (V)$ of smooth complex valued functions on V. Under a mild condition on the tangent spaces, we prove that $C^\infty (V)$ is flat as a module over $O (\tilde V)$. From this we deduce a comparison theorem for the Hochschild homology of finite type algebras over $O (\tilde V)$ and the Hochschild homology of similar algebras over $C^\infty (V)$. We also establish versions of these results for functions on $\tilde V$ (resp. V) that are invariant under the action of a finite group G. As an auxiliary result, we show that $C^\infty (V)$ has finite rank as module over $C^\infty (V)^G$.
