2009/12/21 by Feng-Wen An, An, Feng-Wen
Mathematics · #11G35 #14F35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G35 #msc:14F35
paper · pdf · doi:10.48550/arxiv.0912.4017
48 pages
arxiv created 2009/12/21 · arxiv updated 2010/01/14
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.