Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 6

Shifted symplectic reduction of derived critical loci

Pages: 1543 – 1583



Mathieu Anel (Department of Philosophy, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Damien Calaque (IMAG, Université de Montpellier, CNRS, Montpellier, France)


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.

Published 30 June 2023