Pop, FlorianSilberstein, Aaron2012-12-192012-12-192012Silberstein, Aaron. 2012. Anabelian Intersection Theory. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:10141http://nrs.harvard.edu/urn-3:HUL.InstRepos:10086302Let 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.en-USalgebraic geometryfundamental groupsgroup theoryHodge theorynumber theorytopologymathematicsThesis or Dissertation2012-12-19