Lefschetz type formulas for dg-categories
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Alexander Polishchuk [1]
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[1] University of Oregon
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 3, 2014, págs. 885-928
- Idioma: inglés
- Enlaces
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Resumen
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 Lunts (J Algebra 356:230–256, 2012) that takes the form of a reciprocity law for a pair of commuting endofunctors. As an application, we prove a version of Lefschetz formula proposed by Frenkel and Ngô (Bull Math Sci 1(1):129–199, 2011). Also, we compute explicitly the ingredients of the holomorphic Lefschetz formula for the dg-category of matrix factorizations of an isolated singularity wwww . We apply this formula to get some restrictions on the Betti numbers of a Z/2Z/2 -equivariant module over k[[x1,…,xn]]/(ww)k[[x1,…,xn]]/(ww) in the case when ww(−x)=ww(x)ww(−x)=ww(x) .
