We consider diophantine subsets of function fields of curves and show, roughly speaking, that they are either very small or very large. In particular, this implies that the ring of polynomials k[t] is not a diophantine subset of the field of rational functions k(t) for many fields k.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Diophantine set
- Rationally connected variety