A power structure over the Grothendieck ring of geometric dg categories
Abstract
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 with exponent a linear algebraic group.
Keywords
Cite
@article{arxiv.1709.01678,
title = {A power structure over the Grothendieck ring of geometric dg categories},
author = {Ádám Gyenge},
journal= {arXiv preprint arXiv:1709.01678},
year = {2025}
}
Comments
16 pages. Final version. To appear in the Proceedings of the Edinburgh Mathematical Society