We study the derived critical locus of a function f: [X/G] → 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 dCrit(f) R [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.
Classical BV formalism for group actions
Benini M.;
2023-01-01
Abstract
We study the derived critical locus of a function f: [X/G] → 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 dCrit(f) R [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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