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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1709.01678 |
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| _version_ | 1866910886928580608 |
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| author | Gyenge, Ádám |
| author_facet | Gyenge, Ádám |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_01678 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A power structure over the Grothendieck ring of geometric dg categories Gyenge, Ádám Algebraic Geometry 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. |
| title | A power structure over the Grothendieck ring of geometric dg categories |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1709.01678 |