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arXiv · 1905.02227

On rationally connected varieties over $C_1$ fields of characteristic $0$

Marta Pieropan
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Abstract

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic $0$ is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequences of this result, especially in relation to the $C_1$-conjecture. We also provide evidence that supports the conjecture in dimension $3$ for $C_1$ fields of characteristic $0$.

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Marta Pieropan. 2019-05-06. On rationally connected varieties over $C_1$ fields of characteristic $0$. https://arxiv.org/abs/1905.02227

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