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2017 Rationally connected varieties over the maximally unramified extension of $p$-adic fields
Bradley Duesler, Amanda Knecht
Rocky Mountain J. Math. 47(8): 2605-2617 (2017). DOI: 10.1216/RMJ-2017-47-8-2605

Abstract

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 $C_{2}$ fields. The method of proof utilizes a construction from mathematical logic called the ultraproduct.

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Bradley Duesler. Amanda Knecht. "Rationally connected varieties over the maximally unramified extension of $p$-adic fields." Rocky Mountain J. Math. 47 (8) 2605 - 2617, 2017. https://doi.org/10.1216/RMJ-2017-47-8-2605

Information

Published: 2017
First available in Project Euclid: 3 February 2018

zbMATH: 06840990
MathSciNet: MR3760308
Digital Object Identifier: 10.1216/RMJ-2017-47-8-2605

Subjects:
Primary: 14G05, 14M22

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 8 • 2017
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