Arithmetic geometry of character varieties with regular monodromy

Kamgarpour, Masoud; Nam, GyeongHyeon; Puskás, Anna

doi:10.1090/ert/693

Arithmetic geometry of character varieties with regular monodromy
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by Masoud Kamgarpour, GyeongHyeon Nam and Anna Puskás;

Represent. Theory 29 (2025), 347-378

DOI: https://doi.org/10.1090/ert/693

Published electronically: June 12, 2025

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Abstract:

We count points on a family of smooth character varieties with regular semisimple and regular unipotent monodromies. We show that these varieties are polynomial count and obtain an explicit expression for their $E$-polynomials using complex representation theory of finite reductive groups. As an application, we give an example of a cohomologically rigid representation which is not physically rigid.

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Representation Theory

Arithmetic geometry of character varieties with regular monodromy
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Abstract: