Lefschetz type formulas for dg-categories

Details Lefschetz type formulas for dg-categories Lefschetz type formulas for dg-categories

2011-11-03

arxiv.org/abs/1111.0728v4

Mathematics

Algebraic Geometry

26 pages

Scientific paper

We prove an analog of the holomorphic Lefschetz formula for endofunctors of smooth compact dg-categories. We deduce from it a generalization of the Lefschetz formula of V. Lunts that takes the form of a reciprocity law for a pair of commuting endofunctors. We compute explicitly the ingredients of the holomorphic Lefschetz formula for the dg-category of matrix factorizations of an isolated singularity.

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