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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:719852 |
| Date | January 2015 |
| Creators | Strømmen, Kristian John |
| Contributors | Koenigsmann, Jochen |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ora.ox.ac.uk/objects/uuid:2e444569-a23f-4cee-80a9-0321ae6ad021 |
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