In this paper, we prove a prime-to-p version of Grothendieck’s anabelian conjecture for hyperbolic curves over ﬁnite ﬁelds of characteristic p > 0, whose original (full proﬁnite) version was proved by Tamagawa in the affine case and by Mochizuki in the proper case.
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Mohamed Saïdi, Akio Tamagawa, A Prime-to-<em>p</em> Version of Grothendieck’s Anabelian Conjecture for Hyperbolic Curves over Finite Fields of Characteristic <em>p</em> > 0. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, pp. 135–186DOI 10.2977/PRIMS/1234361157