Categorical DT Theory for Local Surfaces

In this chapter, for a quasi-smooth and QCA derived stack \(\mathfrak {M}\) and a conical closed substack \(\mathcal {Z} \subset \mathcal {N} := t_0(\Omega _{\mathfrak {M}}[-1])\) , we introduce \(\mathbb {C}^{\ast }\) -equivariant DT category for the complement \(\mathcal {N}^{\mathrm {ss}} := \mathcal {N} \setminus \mathcal {Z}\) .