Reconstruction of a variety from $\mathscr{O}[[\hbar]]$-modules

TL;DR

This paper demonstrates that algebraic varieties can be uniquely reconstructed from the derived category of certain formal deformation modules, extending previous foundational results in algebraic geometry.

Contribution

It proves the uniqueness of varieties determined by the derived category of $\

Findings

Varieties are uniquely determined by their derived categories of $\

Generalization of Orlov's theorem to $\

Extension of Bondal and Orlov's results to $\

Abstract

We prove that varieties are uniquely determined by the derived category of $\mathscr{O}[[\hbar]]$-modules with coherent cohomology which is the same as $\mathscr{O}$-modules proved by A. Bondal and D. Orlov. We also generalize a theorem of Orlov.