We extend our previous work  on coherent-constructible correspondence for toric varieties to toric Deligne-Mumford (DM) stacks. Following Borisov et al. , a toric DM stack χΣ is described by a "stacky fan" Σ=(N,Σ,β), where N is a finitely generated abelian group and Σ is a simplicial fan in NR = N Z R. From Σ, we define a conical Lagrangian ΛΣ inside the cotangent T*MRof the dual vector space MRof N R, such that torus-equivariant, coherent sheaves on χΣ are equivalent to constructible sheaves on MR with singular support in ΛΣ. The microlocalization theorem of Nadler and the last author [18, 19] provides an algebro-geometrical description of the Fukaya category of a cotangent bundle T*MR in terms of constructible sheaves on the base MR. This allows us to interpret the main theorem stated earlier as an equivariant version of homological mirror symmetry for toric DM stacks.
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