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This is a continuation of prior work of the author on cosection localizationfor d-manifolds. We construct reduced virtual fundamental classes for derivedmanifolds with surjective cosections and cosection localized virtualfundamental classes for $(-2)$-shifted symplectic derived schemes in largergenerality. Moreover, using recent results of Oh-Thomas, we show that thealgebraic and differential geometric constructions of reduced and cosectionlocalized virtual fundamental classes of $(-2)$-shifted symplectic derivedschemes yield the same result in homology. We obtain applications towards theconstruction and integrality of reduced invariants in Donaldson-Thomas theoryof Calabi-Yau fourfolds.

Cosection Localization for D-Manifolds and $(-2)$-Shifted Symplectic Derived Schemes, Revisited