Lefschetz and Hirzebruch–Riemann–Roch formulas via noncommutative motives

Abstract

V. Lunts has recently established Lefschetz fixed point theorems for Fourier-Mukai functors and dg algebras. In the same vein, D. Shklyarov introduced the noncommutative analogue of the Hirzebruch-Riemman-Roch theorem. In this short article, we see how these constructions and computations formally stem from their motivic counterparts.