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dc.contributor.advisorPop, Florian
dc.contributor.authorSilberstein, Aaron
dc.date.accessioned2012-12-19T21:59:39Z
dc.date.issued2012-12-19
dc.date.submitted2012
dc.identifier.citationSilberstein, Aaron. 2012. Anabelian Intersection Theory. Doctoral dissertation, Harvard University.en_US
dc.identifier.otherhttp://dissertations.umi.com/gsas.harvard:10141en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:10086302
dc.description.abstractLet 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_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dash.licenseLAA
dc.subjectalgebraic geometryen_US
dc.subjectfundamental groupsen_US
dc.subjectgroup theoryen_US
dc.subjectHodge theoryen_US
dc.subjectnumber theoryen_US
dc.subjecttopologyen_US
dc.subjectmathematicsen_US
dc.titleAnabelian Intersection Theoryen_US
dc.typeThesis or Dissertationen_US
dc.date.available2012-12-19T21:59:39Z
thesis.degree.date2012en_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorHarvard Universityen_US
thesis.degree.leveldoctoralen_US
thesis.degree.namePh.D.en_US
dc.contributor.committeeMemberMazur, Barryen_US
dc.contributor.committeeMemberMorel, Sophieen_US


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