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arXiv · 1412.7635

Hilbert specialization results with local conditions

François Legrand
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Abstract

Given a field $k$ of characteristic zero and an indeterminate $T$, the main topic of the paper is the construction 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 $k$ is a number field.

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François Legrand. 2014-12-24. Hilbert specialization results with local conditions. https://arxiv.org/abs/1412.7635

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