Algebraic Anabelian Functors

Details Algebraic Anabelian Functors Algebraic Anabelian Functors

2009-12-21

arxiv.org/abs/0912.4017v1

Mathematics

Algebraic Geometry

48 pages

Scientific paper

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

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