Erschienen in:The Rocky Mountain Journal of Mathematics
Sprache:
Englisch
ISSN:
0035-7596;
1945-3795
Entstehung:
Anmerkungen:
Beschreibung:
<p>A result of Graber, Harris and Starr shows that a rationally connected variety defined over the function field of a curve over the complex numbers always has a rational point. Similarly, a separably rationally connected variety over a finite field or the function field of a curve over any algebraically closed field will have a rational point. Here, we show that rationally connected varieties over the maximally unramified extension of the 𝑝-adics usually, in a precise sense, have rational points. This result is in the spirit of Ax and Kochen's result, which states that the 𝑝-adics are usually 𝐶₂ fields. The method of proof utilizes a construction from mathematical logic called the ultraproduct.</p>