Langlands program for $p$-adic coefficients and the petites camarades conjecture

Abstract

In this paper, we prove that, if Deligne's "petites camarades conjecture" holds, then a Langlands type correspondence holds also for $p$-adic coefficients on a smooth curve over a finite field. We also prove that any overconvergent $F$-isocrystal of rank less than or equal to 2 on a smooth variety is $\iota$-mixed.

References in corpus (1)

• Purity for overconvergence

Cited by in corpus (2)

• Crystalline Chebotarëv density theorems
• Rank 2 Local Systems, Barsotti-Tate Groups, and Shimura Curves