publication . Preprint . 2017

A power structure over the Grothendieck ring of geometric dg categories

Gyenge, Ádám;
Open Access English
  • Published: 06 Sep 2017
We prove the existence of a power structure over the Grothendieck ring of geometric dg categories. We show that a conjecture by Galkin and Shinder (proved recently by Bergh, Gorchinskiy, Larsen, and Lunts) relating the motivic and categorical zeta functions of varieties can be reformulated as a compatibility between the motivic and categorical power structures. Using our power structure we show that the categorical zeta function of a geometric dg category can be expressed as a power with exponent the category itself. We give applications of our results for the generating series associated with Hilbert schemes of points, categorical Adams operations, and series w...
arXiv: Mathematics::Category Theory
free text keywords: Mathematics - Algebraic Geometry
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23 references, page 1 of 2

1. Daniel Bergh, Functorial destackification of tame stacks with abelian stabilisers, Compositio Mathematica 153 (2017), no. 6, 1257-1315.

2. , Weak factorization and the Grothendieck group of Deligne-Mumford stacks, arXiv preprint arXiv:1707.06040 (2017).

3. Daniel Bergh, Sergey Gorchinskiy, Michael Larsen, and Valery Lunts, Categorical measures for finite groups, arXiv preprint arxiv:1709.00620 (2017). [OpenAIRE]

4. Daniel Bergh, Valery A Lunts, and Olaf M Schnu¨rer, Geometricity for derived categories of algebraic stacks, Selecta Mathematica 22 (2016), no. 4, 2535-2568.

5. Franziska Bittner, The universal euler characteristic for varieties of characteristic zero, Compositio Mathematica 140 (2004), no. 4, 1011-1032.

6. A Bondal and D Orlov, Derived categories of coherent sheaves, International Congress of Mathematicians, 2002, p. 47. [OpenAIRE]

7. Alexei I Bondal, Representation of associative algebras and coherent sheaves, Mathematics of the USSR-Izvestiya 34 (1990), no. 1, 23.

8. Alexei I Bondal and Mikhail M Kapranov, Representable functors, serre functors, and mutations, Izvestiya: Mathematics 35 (1990), no. 3, 519-541. [OpenAIRE]

9. Alexey I Bondal, Michael Larsen, and Valery A Lunts, Grothendieck ring of pretriangulated categories, International Mathematics Research Notices 2004 (2004), no. 29, 1461-1495.

10. Sabin Cautis and Anthony Licata, Heisenberg categorification and hilbert schemes, Duke Mathematical Journal 161 (2012), no. 13, 2469-2547.

11. Alexei D Elagin, Cohomological descent theory for a morphism of stacks and for equivariant derived categories, Sbornik: Mathematics 202 (2011), no. 4, 495.

12. Alexei Dmitrievich Elagin, Descent theory for derived categories, Russian Mathematical Surveys 64 (2009), no. 4, 748-749.

13. , Descent theory for semiorthogonal decompositions, Sbornik: Mathematics 203 (2012), no. 5, 645-676.

14. Alexey Elagin, On equivariant triangulated categories, arXiv preprint arXiv:1403.7027 (2014). [OpenAIRE]

15. Sergey Galkin and Evgeny Shinder, On a zeta-function of a dg-category, arXiv preprint arXiv:1506.05831 (2015). [OpenAIRE]

23 references, page 1 of 2
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