Langlands program for p-adic coefficients and the petits camarades conjecture

Abstract

AbstractIn this paper, we prove that, if Deligne’s “petits camarades conjecture” holds, then a Langlands type correspondence holds also forp-adic coefficients on a smooth curve over a finite field. As an application, we prove that any overconvergentF-isocrystal of rank less than or equal to 2 on a smooth curve is ι-mixed.