Arithmetic and representation theory of wild character varieties

T. Hausel, M. Mereb, M. Wong, Journal of the European Mathematical Society 21 (2019) 2995–3052.


Journal Article | Published | English
Department
Abstract
We count points over a finite field on wild character varieties,of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma–Hecke algebras. Our result leads to the conjecture that the mixed Hodge polynomials of these character varieties agree with previously conjectured perverse Hodge polynomials of certain twisted parabolic Higgs moduli spaces, indicating the possibility of a P = W conjecture for a suitable wild Hitchin system.
Publishing Year
Date Published
2019-10-01
Journal Title
Journal of the European Mathematical Society
Volume
21
Issue
10
Page
2995-3052
eISSN
IST-REx-ID

Cite this

Hausel T, Mereb M, Wong M. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 2019;21(10):2995-3052. doi:10.4171/JEMS/896
Hausel, T., Mereb, M., & Wong, M. (2019). Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society, 21(10), 2995–3052. https://doi.org/10.4171/JEMS/896
Hausel, Tamas, Martin Mereb, and Michael Wong. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society 21, no. 10 (2019): 2995–3052. https://doi.org/10.4171/JEMS/896.
T. Hausel, M. Mereb, and M. Wong, “Arithmetic and representation theory of wild character varieties,” Journal of the European Mathematical Society, vol. 21, no. 10, pp. 2995–3052, 2019.
Hausel T, Mereb M, Wong M. 2019. Arithmetic and representation theory of wild character varieties. Journal of the European Mathematical Society. 21(10), 2995–3052.
Hausel, Tamas, et al. “Arithmetic and Representation Theory of Wild Character Varieties.” Journal of the European Mathematical Society, vol. 21, no. 10, European Mathematical Society, 2019, pp. 2995–3052, doi:10.4171/JEMS/896.

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