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We construct a canonical stabilizer reduction $\widetilde{X}$ for any derived$1$-algebraic stack $X$ over $\mathbb{C}$ as a sequence of derived Kirwanblow-ups, under mild natural conditions that include the existence of a goodmoduli space for the classical truncation $X_{\mathrm{cl}}$.  Our construction has several desired features: it naturally generalizesKirwan's classical partial desingularization algorithm to the context ofderived algebraic geometry, preserves quasi-smoothness, and is a derivedenhancement of the intrinsic stabilizer reduction constructed by Kiem, Li andthe third author. Moreover, if $X$ is $(-1)$-shifted symplectic, we show thatthe semi-perfect and almost perfect obstruction theory of$\widetilde{X}_{\mathrm{cl}}$ and the associated virtual fundamental cycle andvirtual structure sheaf, constructed by the same authors, are naturally inducedby $\widetilde{X}$ and its derived tangent complex. As corollaries, we definevirtual classes for moduli stacks of semistable sheaves on surfaces, give afully derived perspective on generalized Donaldson-Thomas invariants ofCalabi-Yau threefolds and define new generalized Vafa-Witten invariants forsurfaces via Kirwan blow-ups.

Stabilizer Reduction for Derived Stacks and Applications to Sheaf-Theoretic Invariants