Hongjie Yu:l-adic local systems, Higgs bundles and Arthur trace formulas

Abstract: Deligne raised the question of counting l-adic local systems on a curve and made some conjectures about it. The global Langlands correspondence proved by L. Lafforgue offers the possibility to do the counting by enumerating some cuspidal automorphic representations which can be done using Arthur's trace formula. From another perspective, Ngô, Chaudoaurd and Laumon observed a relation between the moduli of semi-stable Higgs bundles and a Lie algebra analogue of the trace formula. We relate Arthur's trace formula to its Lie algebra analogue, which implies a numerical relation between Higgs bundles and l-adic local systems and it proves some new cases of Deligne's conjectures.