58:31
published on June 23, 2023
Motivic integration with pseudo-finite residue field and fundamental lemma
By Arthur Forey
Counting $l$-adic local systems over a curve over a finite field
By Hongjie Yu
Appears in collection : Automorphic forms, endoscopy and trace formulas / Formes automorphes, endoscopie et formule des traces
In 1981, Drinfeld enumerated the number of irreducible $l$-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks like the number of points on a variety over a finite field. Deligne proposed conjectures to extend and comprehend Drinfeld's result. By the Langlands correspondence, it is equivalent to count certain cuspidal automorphic representations over a function field. In this talk, I will present some counting results where we connect counting to the number of stable Higgs bundles using Arthur's non-invariant trace formula.
