Hochschild cohomology of deformation quantizations over $\mathbb{Z}/p^n\mathbb{Z}$

Abstract

Let X be a an affine smooth symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and A be its deformation quantization over the p-adic integers. We prove that for all $n\ge 1,$ the Hochschild cohomogy of $A/p^{n}A$ is isomorphic to the de Rham-Witt complex of X over $\mathbb{Z}/p^n\mathbb{Z}$. We also compute centers of deformations of certain affine Poisson varieties over $\mathbb{Z}/p\mathbb{Z}.$

arXiv comment6 pages, all comments welcome

References in corpus (1)

• Localization of modules for a semisimple Lie algebra in prime characteristic

Cited by in corpus (1)

• Ideals in deformation quantizations over $\mathbb{Z}/p^n\mathbb{Z}$