Vol. 2, No. 3, 2008

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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[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