Categorical measures for finite group actions
| Autor: | Michael Larsen, Valery A. Lunts, Sergey Gorchinskiy, Daniel Bergh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Finite group Algebra and Number Theory Conjecture 010102 general mathematics 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Measure (mathematics) Quotient stack Mathematics - Algebraic Geometry FOS: Mathematics Equivariant map Geometry and Topology 0101 mathematics Variety (universal algebra) 0210 nano-technology Algebraic Geometry (math.AG) Categorical variable Quotient Mathematics |
| Zdroj: | Bergh, D, Gorchinskiy, S, Larsen, M & Lunts, V 2021, ' Categorical measures for finite group actions ', Journal of Algebraic Geometry, vol. 30, no. 4, pp. 685-757 . https://doi.org/10.1090/jag/768 Journal of Algebraic Geometry |
| DOI: | 10.1090/jag/768 |
| Popis: | Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases, these two measures coincide. This implies, in particular, a conjecture of Galkin and Shinder on categorical and motivic zeta-functions of varieties. We provide examples showing that, in general, these two measures are not equal. We also give an example related to a conjecture of Polishchuk and Van den Bergh, showing that a certain condition in this conjecture is indeed necessary. 55 pages. Comments are welcome |
| Databáze: | OpenAIRE |
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