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arXiv · 1703.08334

Rational points of rationally simply connected varieties over global function fields

Jason Starr·Chenyang Xu
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Abstract

A complex projective manifold is rationally connected, resp. rationally simply connected, if finite subsets are connected by a rational curve, resp. the spaces parameterizing these connecting rational curves are themselves rationally connected. We prove that a projective scheme over a global function field with vanishing "elementary obstruction" has a rational point if it deforms to a rationally simply connected variety in characteristic 0. This gives new, uniform proofs over these fields of the Period-Index Theorem, the quasi-split case of Serre's "Conjecture II", and Lang's $C_2$ property.

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Jason Starr, Chenyang Xu. 2017-03-24. Rational points of rationally simply connected varieties over global function fields. https://arxiv.org/abs/1703.08334

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