| 概要 | The Hochschild homology and cohomology of an algebraic variety
were defined by Swan. In the smooth case the
Hochschild-Kostant-Rosenberg theorem yields
a kind of Hodge decomposition for these invariants.
Unfortunately the HKR decomposition does not
respect the many additional structures present on Hochschild
(co)homology (cupproduct, Lie bracket, capproduct,...).
In 2003 Caldararu conjectured (following a suggestion by
Kontsevich) that the HKR morphism could be made to
preserve the additional structures provided it is corrected
in a suitable way.
In the talk I will outline a proof of this conjecture using
deformation quantization. This is joint work with
Damien Calaque and Carlo Rossi. |