Classical BV formalism for group actions

We study the derived critical locus of a function f : [ X/G ] → A 1 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 ] 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

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