On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

doi:10.48550/arXiv.1905.02227

On rationally connected varieties over C1 fields of characteristic 0

Research output: Working paper › Preprint › Academic

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 C1-conjecture. We also provide evidence that supports the conjecture in dimension 3 for C1 fields of characteristic 0.

Original language	English
Publisher	arXiv
Pages	1-30
DOIs	https://doi.org/10.48550/arXiv.1905.02227
Publication status	Published - 5 Aug 2021

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10.48550/arXiv.1905.02227

1905.02227v2Submitted manuscript, 473 KB

https://arxiv.org/abs/1905.02227

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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 C1-conjecture. We also provide evidence that supports the conjecture in dimension 3 for C1 fields of characteristic 0.",

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AB - 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 C1-conjecture. We also provide evidence that supports the conjecture in dimension 3 for C1 fields of characteristic 0.

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On rationally connected varieties over C1 fields of characteristic 0

Abstract

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