The nonequivariant coherent-constructible correspondence for toric stacks

Abstract

The nonequivariant coherent-constructible correspondence is a microlocal-geometric interpretation of homological mirror symmetry for toric varieties conjectured by Fang, Liu, Treumann, and Zaslow. We prove a generalization of this conjecture for a class of toric stacks which includes any toric variety and toric orbifold. Our proof is based on gluing descriptions of $\infty$-categories of both sides.