Submission date: 26 July 2020

Abstract:

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)

Keywords and phrases:

Full text arXiv 2007.13047: pdf, ps.