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

Abstract

Let $X$ be a smooth affine symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and let $A_1$ be an Azumaya algebra over $X.$ In this note we show that if $A$ is a deformation quantization of $A_1$ over $\mathbb{Z}/p^n\mathbb{Z}$, then any two-sided $\mathbb{Z}/p^n\mathbb{Z}$-flat ideal in $A$ is generated by central elements.

8 pages, to appear in Journal of Pure and Applied Algebra

References in corpus (2)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• Hochschild cohomology of deformation quantizations over $\mathbb{Z}/p^n\mathbb{Z}$