• Corpus ID: 220793933

# Hilbert's Tenth Problem and the Inverse Galois Problem

@article{Balestrieri2020HilbertsTP,
title={Hilbert's Tenth Problem and the Inverse Galois Problem},
author={Francesca Balestrieri and Jennifer Park and Alexandra Shlapentokh},
journal={arXiv: Number Theory},
year={2020}
}
• Published 26 July 2020
• Mathematics
• arXiv: Number Theory
We show that the inverse Galois problem over global fields can be reduced to Hilbert's tenth problem over $\mathbb{Q}$ (and consequently over $\mathbb{Z}$); that is, if there is an algorithm to decide the existence of a solution for an arbitrary polynomial equation over $\mathbb{Q}$, then there is an algorithm to decide whether a certain group $G$ appears as the Galois group of a finite extension of a given global field $K$.

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