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arXiv · 2010.14024

Existential decidability for addition and divisibility in holomorphy subrings of global fields

Carlos Martinez-Ranero·Javier Utreras·Xavier Vidaux
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Abstract

We investigate the problem of deciding whether a system of linear equations, together with divisibility conditions on the variables, has a solution over holomorphy subrings of global fields. We obtain decidability results when we allow poles at a cofinite set of places, and undecidability results when at a finite set of places.

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Carlos Martinez-Ranero, Javier Utreras, Xavier Vidaux. 2020-10-27. Existential decidability for addition and divisibility in holomorphy subrings of global fields. https://arxiv.org/abs/2010.14024

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