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

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