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.

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