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Localization in Hochschild homology

Markus J. Pflaum
Aug 2022
摘要
Localization methods are ubiquitous in cyclic homology theory, but vary indetail and are used in different scenarios. In this paper we will elaborate ona common feature of localization methods in noncommutative geometry, namelysheafification of the algebra under consideration and reduction of thecomputation to the stalks of the sheaf. The novelty of our approach lies in themethods we use which mainly stem from real instead of complex algebraicgeometry. We will then indicate how this method can be used to determine theHochschild homology theory of more complicated algebras out of simpler ones.
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