Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 21, Issue 10, Pages 2995-3052Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/896
Keywords
Irregular connection; character variety; Hitchin system; Yokonuma-Hecke algebra; Macdonald polynomials
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Funding
- Ecole Polytechnique Federale de Lausanne
- Advanced Grant Arithmetic and physics of Higgs moduli spaces of the European Research Council [320593]
- NCCR SwissMAP of the Swiss National Foundation
- [SFB/TR 45]
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We count points over a finite field on wild character varieties of Riemann surfaces for singularities with regular semisimple leading term. A 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 the 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.
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