## Abstract

Let X be a smooth separated scheme over a noetherian base ring K. The decomposition we are interested in is an isomorphism R ℋom_{oX×KX}(O_{X}, O_{X}) ≅ ⊕_{q} (Λ_{ox}^{q} τ_{X/K})[-q] in the derived category D(Mod O_{x × K} x). Here τ_{X/K} is the relative tangent sheaf. Upon passing to cohomology sheaves such an isomorphism recovers the Hochschild-Kostant-Rosenberg Theorem. If K has characteristic 0 there is a decomposition that relies on a particular homomorphism of complexes from poly-tangents to continuous Hochschild cochains. We discuss sheaves of continuous Hochschild cochains on schemes and show why this approach to decomposition fails in positive characteristics. Our main result is a proof of the decomposition valid for any Gorenstein noetherian ring K of finite Krull dimension, regardless of characteristic. The proof is based on properties of minimal injective resolutions.

Original language | English |
---|---|

Pages (from-to) | 866-896 |

Number of pages | 31 |

Journal | Canadian Journal of Mathematics |

Volume | 54 |

Issue number | 4 |

State | Published - 1 Aug 2002 |

## Keywords

- Derived categories
- Gorenstein rings
- Hochschild cohomology
- Schemes