2 citations · 8 across the 10 of their papers we have counts for
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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…
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…
Defining in
Jochen Koenigsmann
We show that is definable in by a universal first-order formula in the language of rings. We also present an -formula for …
Relatively projective groups as absolute Galois groups
Jochen Koenigsmann
By two well-known results, one of Ax, one of Lubotzky and van den Dries, a profinite group is projective iff it is isomorphic to the absolute Galois group of a pseudo-algebraically…