2 citations · 8 across the 10 of their papers we have counts for
13 papers
The Galois characterisation of -adically closed fields -- A modern perspective
Leo Gitin, Jochen Koenigsmann, Benedikt Stock
In 1927, Artin and Schreier showed that a field is real closed if and only if its absolute Galois group has order two. Inspired by this characterisation and drawing on earlier work…
An elementary proof of the local Kronecker-Weber theorem
Jochen Koenigsmann, Benedikt Stock
We will present a novel elementary, self-contained, and explicit proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools…
Recovering p-adic valuations from pro-p Galois groups
Jochen Koenigsmann, Kristian Strommen
Let be a field with , where denotes the maximal pro-2 quotient of the absolute Galois group of a field . We prove that then adm…
Defining coarsenings of valuations
Franziska Jahnke, Jochen Koenigsmann
We study the question which henselian fields admit definable henselian valuations (with or without parameters). We show that every field which admits a henselian valuation with non…
Uniformly defining -henselian valuations
Franziska Jahnke, Jochen Koenigsmann
Admitting a non-trivial -henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, -henselianity is an elem…
Undecidability in number theory
Jochen Koenigsmann
These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It al…