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 Behrend, K. The Lefschetz Trace Formula for the Moduli Stack of Principal Bundles. PhD dissertation. 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.
