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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/14299

Title: Caldararu's conjecture and Tsygan's formality
Authors: Calaque, Damien
Rossi, Carlo A.
Van den Bergh, Michel
Issue Date: 2012
Publisher: ANNAL MATHEMATICS
Citation: ANNALS OF MATHEMATICS, 176 (2), p. 865-923
Abstract: In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over polyvector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet. (The existence of the latter was conjectured by Tsygan.) We also rely on the fact - recently proved by the first two authors - that Shoikhet's quasi-isomorphism is compatible with cap products after twisting with a Maurer-Cartan element.
Notes: [Calaque, Damien] ETH, Zurich, Switzerland. [Calaque, Damien] CNRS, Inst Camille Jordan, F-75700 Paris, France. [Calaque, Damien] Univ Lyon 1, F-69622 Villeurbanne, France. [Rossi, Carlo A.] MPIM Bonn, Bonn, Germany. [Van den Bergh, Michel] Hasselt Univ, Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/14299
DOI: 10.4007/annals.2012.176.2.4
ISI #: 000307878000004
ISSN: 0003-486X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Algebra

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