2012/11/18 by Vasily Dolgushev, Dolgushev, Vasily, Christopher L. Rogers +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.AG #math.KT #math.QA
paper · pdf · doi:10.48550/arxiv.1211.4230
The final version will appear in Annals of Mathematics
arxiv created 2015/02/06 · arxiv updated 2015/02/09
We generalize Kontsevich's construction of L-infinity derivations of polyvector fields from the affine space to an arbitrary smooth algebraic variety. More precisely, we construct a map (in the homotopy category) from Kontsevich's graph complex to the deformation complex of the sheaf of polyvector fields on a smooth algebraic variety. We show that the action of Deligne-Drinfeld elements of the Grothendieck-Teichmueller Lie algebra on the cohomology of the sheaf of polyvector fields coincides with the action of odd components of the Chern character. Using this result, we deduce that the A-hat genus in the Calaque-Van den Bergh formula arXiv:0708.2725 for the isomorphism between harmonic and Hochschild structures can be replaced by a generalized A-hat genus.