Abstract

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.

Keywords

diophantine set, rationally connected variety

Mathematical Subject Classification

Primary: 11U05

Secondary: 14G25, 14M20, 14G27

Authors