Anabelian Intersection Theory
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Silberstein, Aaron
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Silberstein, Aaron. 2012. Anabelian Intersection Theory. Doctoral dissertation, Harvard University.Abstract
Let F be a field finitely generated and of transcendence degree 2 over \(\bar{\mathbb{Q}}\). We describe a correspondence between the smooth algebraic surfaces X defined over \(\bar{\mathbb{Q}}\) with field of rational functions F and Florian Pop’s geometric sets of prime divisors on \(Gal(\bar{F}/F)\), which are purely group-theoretical objects. This allows us to give a strong anabelian theorem for these surfaces. As a corollary, for each number field K, we give a method to construct infinitely many profinite groups \(\Gamma\) such that \(Out_{cont} (\Gamma)\) is isomorphic to \(Gal(\bar{K}/K)\), and we find a host of new categories which answer the Question of Ihara/Conjecture of Oda-Matsumura.Terms of Use
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