# Classical BV formalism for group actions

Marco Benini, Pavel Safronov, Alexander Schenkel
April 30, 2021
We study the derived critical locus of a function $f:[X/G]\to \mathbb{A}_{\mathbb{K}}^1$ on the quotient stack of a smooth affine scheme $X$ by the action of a smooth affine group scheme $G$. It is shown that $\mathrm{dCrit}(f) \simeq [Z/G]$ is a derived quotient stack for a derived affine scheme $Z$, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.

Keywords:
Derived algebraic geometry, derived critical locus, quotient stack, Batalin-Vilkovisky formalism