Langlands program for $p$-adic coefficients and the petites camarades   conjecture
  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. 
Tomoyuki Abe
math.AG