| Literatur |
- Engler, Prestel: Valued Fields, Springer, 2005.
- Koenigsmann, Jochen. "From p-rigid elements to valuations (with a Galois-characterization of p-adic fields).", J. reine angew. Math. (465), 1995, pp. 165-182.
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| Lerninhalte |
The absolute Galois group of a field K is the group of automorphims of the algebraic closure of K that fix K pointwise. In this seminar, we study fields K whose absolute Galois group is isomorphic to that of the field of the p-adic numbers. The aim of the seminar is to show that any such field admits an unramified henselian valuation of mixed characteristic with finite residue field of cardinality p taking values in a Z-group, i.e., K is elementarily equivalent to the field of p-adic numbers. |
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