Galois groups and anabelian reconstruction

Thesis

In this thesis we investigate the problem of recovering arithmetic structure on a field F from small quotients of its absolute Galois group. In particular, we are interested in recovering the p-adic valuation on a p-adic field from such quotients. After establishing several such results, we apply this to obtain strong versions of the Birational Section Conjecture for curves over p-adic fields. We also discuss the model-theoretic interpretation of these results, as well as begin investigating the foundations of a model-theory of schemes.

Authors: Strommen, K

• DOI: 10.5287/ora-zbnde0nrv
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Anabelian Geometry; p-adic arithmetic; Valued Fields; Galois Theory
• Subjects: Mathematics