Dimensional reduction in cohomological Donaldson–Thomas theory

For oriented $-1$ -shifted symplectic derived Artin stacks, Ben-Bassat, Brav, Bussi and Joyce introduced certain perverse sheaves on them which can be regarded as sheaf-theoretic categorifications of the Donaldson–Thomas invariants. In this paper, we prove that hypercohomology above sheaf cotangent stack over a quasi-smooth is isomorphic to Borel–Moore homology base up shift degree. This global version dimensional reduction theorem due Davison. We give two applications our main theorem. Firstly, apply it study cohomological invariants for local surfaces. Secondly, regarding Thom isomorphism dual obstruction cones, propose construction virtual fundamental classes stacks.