Skip to Main content Skip to Navigation

Comptage des systèmes locaux ℓ-adiques sur une courbe

Abstract : Let X1 be a projective, smooth and geometrically connected curve over Fq with q = pn 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 ℓ-adic local systems (ℓ ≠ 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.
Document type :
Complete list of metadata

Cited literature [53 references]  Display  Hide  Download
Contributor : Abes Star :  Contact
Submitted on : Friday, June 28, 2019 - 11:30:08 AM
Last modification on : Monday, December 14, 2020 - 9:44:32 AM


Version validated by the jury (STAR)


  • HAL Id : tel-02167864, version 1


Hongjie Yu. Comptage des systèmes locaux ℓ-adiques sur une courbe. Mathématiques générales [math.GM]. Université Sorbonne Paris Cité, 2018. Français. ⟨NNT : 2018USPCC057⟩. ⟨tel-02167864⟩



Record views


Files downloads