Shifted symplectic reduction of derived critical loci

Abstract

We prove that the derived critical locus of a $G$-invariant function $S:X\to {\mathbb{A}}^1$ carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function $S_{red}:X/G\to {\mathbb{A}}^1$ on the orbit stack. We also provide a relative version of this result, and show that derived symplectic reduction commutes with derived lagrangian intersections.

final version, appeared in ATMP

References in corpus (4)

• Higher Topos Theory
• Relative critical loci and quiver moduli
• The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory
• Classical BV formalism for group actions

Cited by in corpus (2)

• Relative critical loci and quiver moduli
• Shifted coisotropic structures for differentiable stacks