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Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve, .(., ℂ) vs. .(., ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmeti痛苦一生 发表于 2025-3-22 07:21:58
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https://doi.org/10.1007/978-3-0348-5310-1We discuss the enumeration of function fields and number fields by discriminant. We show that Malle’s conjectures agree with heuristics arising naturally from geometric computations on Hurwitz schemes. These heuristics also suggest further questions in the number field setting.