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Abstract: In this paper we will prove that there exists a covariant functor, calledalgebraic anabelian functor, from the category of algebraic schemes over agiven field to the category of outer homomorphism sets of groups. The algebraicanabelian functor, given in a canonical manner, is full and faithful. Itreformulates the anabelian geometry over a field. As an application of theanabelian functor, we will also give a proof of the section conjecture ofGrothendieck for the case of algebraic schemes.

Author: Feng-Wen An


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