## Rocky Mountain Journal of Mathematics

### Hilbert specialization results with local conditions

François Legrand

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 21 November 2017

https://projecteuclid.org/euclid.rmjm/1511254958

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-1917

Mathematical Reviews number (MathSciNet)
MR3725250

Zentralblatt MATH identifier
06816576

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1511254958