# Anabelian Intersection Theory

 Title: Anabelian Intersection Theory Author: Silberstein, Aaron Citation: Silberstein, Aaron. 2012. Anabelian Intersection Theory. Doctoral dissertation, Harvard University. Full Text & Related Files: Silberstein_gsas.harvard_0084L_10141.pdf (613.9Kb; PDF) 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: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10086302 Downloads of this work: