Comptage des syst?mes locaux l-adiques sur une courbe

• 成果类型: Article
• 署名作者: Yu, Hongjie
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.197.2.1
• 发表日期: 2023
• 页码: 423-531
• 关键词: trace formula; zeta-function; moduli space; unipotent; motives; systems; FIELDS; FAMILY

摘要

Let X1 be a projective, smooth and geometrically connected curve over Fq with q = p' elements where p is a prime number, and let X be its base change to an algebraic closure of Fq. We give a formula for the number of irreducible B-adic local systems (B =6 p) with a fixed rank over X fixed by the Frobenius endomorphism. We prove that this number behaves like a Lefschetz fixed point formula for a variety over Fq, which generalises a result of Drinfeld in rank 2 and proves a conjecture of Deligne. To do this, we pass to the automorphic side by Langlands correspondence, then use Arthur's non-invariant trace formula and link this number to the number of Fq-points of the moduli space of stable Higgs bundles.