Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0
| dc.creator | Moret-Bailly, Laurent | |
| dc.creator | Shlapentokh, Alexandra | |
| dc.date | 2008-05-22 | |
| dc.date | 2009-01-19 | |
| dc.date.accessioned | 2026-07-07T12:30:53Z | |
| dc.date.available | 2026-07-07T12:30:53Z | |
| dc.description | Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$, not equal to $K$. We prove the following undecidability results for $R$: If $K$ is recursive, then Hilbert's Tenth Problem is undecidable in $R$. In general, there exist $x_1,...,x_n \in R$ such that there is no algorithm to tell whether a polynomial equation with coefficients in $\Q(x_1,...,x_n)$ has solutions in $R$. | |
| dc.description | This version contains minor revisions and will appear in Annales de l Institut Fourier | |
| dc.identifier | https://arxiv.org/abs/0805.3458 | |
| dc.identifier | http://arxiv.org/abs/0805.3458 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216271 | |
| dc.subject | Logic | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 11U05, 03D35, 11G05 | |
| dc.title | Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0 | |
| dc.type | text |