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In this paper, we prove a prime-to-p version of Grothendieck's anabelianconjecture for hyperbolic curves over finite fields of characteristic p>0,whose original (full profinite) version was proved by Tamagawa in the affinecase and by Mochizuki in the proper case.

A prime-to-p version of the Grothendieck anabelian conjecture for hyperbolic curves over finite fields of characteristic p>0