We study the derived critical locus of a function f: [X/G] → A1K 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.
Classical BV formalism for group actions / Benini, Marco; Safronov, Pavel; Schenkel, Alexander. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 25:01(2021). [10.1142/s0219199721500942]
Classical BV formalism for group actions
Schenkel, Alexander
2021-01-01
Abstract
We study the derived critical locus of a function f: [X/G] → A1K 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.File in questo prodotto:
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