#### Vol. 2, No. 3, 2008

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Diophantine subsets of function fields of curves

### János Kollár

Vol. 2 (2008), No. 3, 299–311
##### 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 $k\left[t\right]$ is not a diophantine subset of the field of rational functions $k\left(t\right)$ for many fields $k$.

##### Keywords
diophantine set, rationally connected variety
##### Mathematical Subject Classification 2000
Primary: 11U05
Secondary: 14G25, 14M20, 14G27