Lefschetz and Hirzebruch-Riemann-Roch formulas via noncommutative motives

Denis-Charles Cisinski (1) , Goncalo Tabuada (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 MIT - Massachusetts Institute of Technology

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-Riemann-Roch theorem. In this note, making use of the theory of noncommutative motives, we show how these beautiful theorems can be understood as instantiations of more general results.

Domaines: Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; K-théorie et homologie [math.KT]

Denis-Charles Cisinski, Goncalo Tabuada. Lefschetz and Hirzebruch-Riemann-Roch formulas via noncommutative motives. 2011. ⟨hal-00638511⟩