Rocky Mountain Journal of Mathematics

Hilbert specialization results with local conditions

François Legrand

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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.

Article information

Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1917-1945.

First available in Project Euclid: 21 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX] 12E25: Hilbertian fields; Hilbert's irreducibility theorem 12E30: Field arithmetic
Secondary: 14E22: Ramification problems [See also 11S15]

Field extensions specializations local behavior Hilbertian fields


Legrand, François. Hilbert specialization results with local conditions. Rocky Mountain J. Math. 47 (2017), no. 6, 1917--1945. doi:10.1216/RMJ-2017-47-6-1917.

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