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Journal of Noncommutative Geometry

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Volume 8, Issue 4, 2014, pp. 1171–1190
DOI: 10.4171/JNCG/183

Published online: 2015-02-02

Lefschetz and Hirzebruch–Riemann–Roch formulas via noncommutative motives

Denis-Charles Cisinski[1] and Gonçalo Tabuada[2]

(1) Université Paul Sabatier, Toulouse, France
(2) Massachusetts Institute of Technology, Cambridge, USA

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.

Keywords: Lefschetz formula, Hirzebruch–Riemann–Roch formula, Euler characteristic, Fourier–Mukai functors, noncommutative motives

Cisinski Denis-Charles, Tabuada Gonçalo: Lefschetz and Hirzebruch–Riemann–Roch formulas via noncommutative motives. J. Noncommut. Geom. 8 (2014), 1171-1190. doi: 10.4171/JNCG/183