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Preprint Number 1821

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1821. Francesca Balestrieri, Jennifer Park, Alexandra Shlapentokh
Hilbert's Tenth Problem and the Inverse Galois Problem

Submission date: 26 July 2020


We show that the inverse Galois problem over global fields can be reduced to Hilbert's tenth problem over ℚ (and consequently over ℤ); that is, if there is an algorithm to decide the existence of a solution for an arbitrary polynomial equation over 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.

Mathematics Subject Classification: 11U05 (Primary) 12F12, 12L05 (Secondary)

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Full text arXiv 2007.13047: pdf, ps.

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