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A power structure over the Grothendieck ring of geometric dg categories
Published online by Cambridge University Press: 05 December 2024
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 68 , Issue 1 , February 2025 , pp. 300 - 318
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
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