Anabelian Intersection Theory
Year: 2012
Type: dissertation
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.
Author: Aaron Michael Silberstein
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2154543771