Lefschetz fixed point theorems for Fourier-Mukai functors and DG algebras
Valery A. Lunts
TL;DR
This paper extends Lefschetz fixed point theorems to Fourier-Mukai functors on algebraic varieties and endo-functors on perfect modules over DG algebras, providing new theoretical insights.
Contribution
It introduces variants of Lefschetz fixed point theorems applicable to Fourier-Mukai functors and DG algebra modules, broadening the theorem's scope.
Findings
Variants of Lefschetz fixed point theorem for Fourier-Mukai functors
Similar fixed point theorem for endo-functors on DG algebra modules
Theoretical framework connecting algebraic geometry and DG algebra categories
Abstract
We propose some variants of Lefschetz fixed point theorem for Fourier-Mukai functors on a smooth projective algebraic variety. Independently we also suggest a similar theorem for endo-functors on the category of perfect modules over a smooth and proper DG algebra.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra