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2017 Hilbert specialization results with local conditions
François Legrand
Rocky Mountain J. Math. 47(6): 1917-1945 (2017). DOI: 10.1216/RMJ-2017-47-6-1917

Abstract

Given a field $k$ of characteristic~$0$ and~an indeterminate $T$, the main topic of this paper is the con\-struction of specializations of any given finite extension of $k(T)$ of degree~$n$ that are degree~$n$ field extensions of~$k$ with specified local behavior at any given finite set of primes of~$k$. First, we give a full non-Galois analog of a result with a ramified-type conclusion from a preceding paper, and next we prove a unifying statement which combines our results and previous work devoted to the unramified part of the problem in the case where $k$ is a number field.

Citation

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François Legrand. "Hilbert specialization results with local conditions." Rocky Mountain J. Math. 47 (6) 1917 - 1945, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1917

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06816576
MathSciNet: MR3725250
Digital Object Identifier: 10.1216/RMJ-2017-47-6-1917

Subjects:
Primary: 11R58, 12E25, 12E30
Secondary: 14E22

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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