# Shifted symplectic reduction of derived critical loci

@inproceedings{Anel2021ShiftedSR, title={Shifted symplectic reduction of derived critical loci}, author={Mathieu Anel and Damien Calaque}, year={2021} }

We prove that the derived critical locus of a G-invariant function S : X → A carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function Sred : X/G → 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.

## 4 Citations

Classical BV formalism for group actions

- MathematicsCommunications in Contemporary Mathematics
- 2021

We study the derived critical locus of a function f : [X/G] → A K on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) ≃ [Z/G]…

Shifted symplectic higher Lie groupoids and classifying spaces

- Mathematics
- 2021

We introduce the concept of m-shifted symplectic Lie n-groupoids and symplectic Morita equivalences between them. We then build various models for the 2-shifted symplectic structure on the…

Relative critical loci and quiver moduli

- Mathematics
- 2020

In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More…

Quantization of derived cotangent stacks and gauge theory on directed graphs

- Mathematics
- 2022

We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack T ∗[X/G] of a quotient stack, where X is a smooth affine scheme with an action of a (reductive)…

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