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About: Behrend's trace formula     Goto   Sponge   NotDistinct   Permalink

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In algebraic geometry, Behrend's trace formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field, conjectured in 1993 and proven in 2003 by Kai Behrend. Unlike the classical one, the formula counts points in the "stacky way"; it takes into account the presence of nontrivial automorphisms. Pierre Deligne found an example that shows the formula may be interpreted as a sort of the Selberg trace formula.