Diophantine subsets of function fields of curves

Kollár, János

doi:10.2140/ant.2008.2.299

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Diophantine subsets of function fields of curves

János Kollár

Vol. 2 (2008), No. 3, 299–311

DOI: 10.2140/ant.2008.2.299

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 2000

Primary: 11U05

Secondary: 14G25, 14M20, 14G27

Milestones

Received: 26 September 2007

Revised: 16 January 2008

Accepted: 14 February 2008

Published: 1 May 2008

Authors

János Kollár
Department of Mathematics Princeton University Princeton, NJ 08544-1000 United States

Vol. 2, No. 3, 2008