E-polinomios de variedades de caracteres
DOI:
https://doi.org/10.15517/tvetzr54Palabras clave:
Variedades de caracteres, e-polinomios, Estructuras de Hodge mixtas, Simetría especular topológica, Dualidad de LanglandsResumen
Este trabajo contiene las ideas básicas y construcciones sobre e-polinomios en variedades de caracteres y el estado del arte de cierta investigación en el campo, junto con algunas nuevas direcciones. En él introducimos las estructuras de Hodge mixtas y los E-polinomios, junto con una serie de técnicas aritméticas (contar puntos sobre cuerpos finitos) y geométricas (estratificaciones en tipos parabólicos) para calcularlos. Incluimos un ejemplo completo del cálculo del e-polinomio para la GL3-variedad de caracteres del grupo libre. Finalmente, extendemos la estratificación geométrica en tipos parabólicos a un grupo reductivo G general para obtener expresiones motívicas explícitas para la G-variedad de caracteres, y reducir ciertas conjeturas en simetría especular topológica para estos espacios de móduli.
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