Lefschetz and Hirzebruch-Riemann-Roch formulas via noncommutative motives

2011/11/01 by Denis-Charles Cisinski, Cisinski, Denis-Charles, Gonçalo Tabuada +2 · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.KT #msc:14A22 #msc:14C20 #msc:14F25 #msc:14F40 #msc:18D20 #msc:19L10

paper · pdf · doi:10.48550/arxiv.1111.0257

16 pages; revised version

arxiv created 2013/03/20 · arxiv updated 2013/03/22

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-Riemann-Roch theorem. In this short article, we see how these constructions and computations formally stem from their motivic counterparts.

Cited by

• Lefschetz type formulas for dg-categories
• The Lefschetz–Lunts formula for deformation quantization modules

Related

• Lefschetz fixed point theorems for Fourier-Mukai functors and DG algebras
• Noncommutative motives and their applications
• Recent developments on noncommutative motives
• Weil transfer of noncommutative motives
• Noncommutative geometry and motives (a quoi servent les endomotifs?)