Zobrazeno 1 - 10
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pro vyhledávání: '"Koenigsmann, Jochen"'
Autor:
Koenigsmann, Jochen, Stock, Benedikt
We will present a novel elementary and self-contained proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on algebra. In particul
Externí odkaz:
http://arxiv.org/abs/2206.05801
Akademický článek
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Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}}(2)$, where $G_F(2)$ denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$. We prove that then $K$ admits a (non-trivial) valuation $v$ which is 2-henselian and has residue
Externí odkaz:
http://arxiv.org/abs/1506.05956
Autor:
Jahnke, Franziska, Koenigsmann, Jochen
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-divisible value group admits a parameter-definable (non-trivial) hens
Externí odkaz:
http://arxiv.org/abs/1501.04506
Autor:
Jahnke, Franziska, Koenigsmann, Jochen
Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the que
Externí odkaz:
http://arxiv.org/abs/1407.8156
Autor:
Koenigsmann, Jochen
In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable. We construct 'natural' undecidable fields of transcendence degree 1 over Q all of whose proper
Externí odkaz:
http://arxiv.org/abs/1309.7138
Autor:
Koenigsmann, Jochen
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 also contains a sketch of the authors result that the integers are unive
Externí odkaz:
http://arxiv.org/abs/1309.0441
Autor:
Anscombe, Will, Koenigsmann, Jochen
We show that the valuation ring F_q[[t]] in the local field F_q((t)) is existentially definable in the language of rings with no parameters. The method is to use the definition of the henselian topology following the work of Prestel-Ziegler to give a
Externí odkaz:
http://arxiv.org/abs/1306.6760
Autor:
Jahnke, Franziska, Koenigsmann, Jochen
In this note we investigate the question whether a henselian valued field carries a non-trivial 0-definable henselian valuation (in the language of rings). It follows from the work of Prestel and Ziegler that there are henselian valued fields which d
Externí odkaz:
http://arxiv.org/abs/1210.7615
Autor:
Koenigsmann, Jochen
We show that ${\mathbb Z}$ is definable in ${\mathbb Q}$ by a universal first-order formula in the language of rings. We also present an $\forall\exists$-formula for ${\mathbb Z}$ in ${\mathbb Q}$ with just one universal quantifier. We exhibit new di
Externí odkaz:
http://arxiv.org/abs/1011.3424