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 article, we see how these constructions and computations formally stem from their motivic counterparts.