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2020 Motivic random variables and representation stability, I: Configuration spaces
Sean Howe
Algebr. Geom. Topol. 20(6): 3013-3045 (2020). DOI: 10.2140/agt.2020.20.3013

Abstract

We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over attached to character polynomials. Our approach interprets the stabilization as a probabilistic phenomenon based on the asymptotic independence of certain motivic random variables, and gives explicit universal formulas for the limits in terms of the exponents of a motivic Euler product for the Kapranov zeta function. The result can be thought of as a weak but explicit version of representation stability for the cohomology of ordered configuration spaces. In the sequel, we find similar stability results in spaces of smooth hypersurface sections, providing new examples to be investigated through the lens of representation stability for symmetric, symplectic and orthogonal groups.

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Sean Howe. "Motivic random variables and representation stability, I: Configuration spaces." Algebr. Geom. Topol. 20 (6) 3013 - 3045, 2020. https://doi.org/10.2140/agt.2020.20.3013

Information

Received: 14 April 2019; Revised: 27 November 2019; Accepted: 10 March 2020; Published: 2020
First available in Project Euclid: 16 December 2020

MathSciNet: MR4185934
Digital Object Identifier: 10.2140/agt.2020.20.3013

Subjects:
Primary: 14G10, 18F30, 55R80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 6 • 2020
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