A Hochschild-Kostant-Rosenberg theorem for cyclic homology

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• 作者：Marcel Bö ; kstedt^a ; ^{marcel@math.au.dk} ; Iver Ottosen^b ; ^{ottosen@math.aau.dk}
• 关键词：19D55 ; 18G50
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：221
• 期：6
• 页码：1458-1493
• 全文大小：600 K
• 卷排序：221

文摘

Let A   be a commutative algebra over the field F2=Z/2F2=Z/2. We show that there is a natural algebra homomorphism ℓ(A)→HC⁎−(A) which is an isomorphism when A is a smooth algebra. Thus, the functor ℓ   can be viewed as an approximation of negative cyclic homology and ordinary cyclic homology HC⁎(A)HC⁎(A) is a natural ℓ(A)ℓ(A)-module. In general, there is a spectral sequence E2=L⁎(ℓ)(A)⇒HC⁎−(A). We find associated approximation functors ℓ^{+ℓ+ and ℓperℓper for ordinary cyclic homology and periodic cyclic homology, and set up their spectral sequences. Finally, we discuss universality of the approximations.}