On rationally connected varieties over C1 fields of characteristic 0

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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.
Original languageEnglish
Pages (from-to)1811-1844
Number of pages34
JournalAlgebra Number Theory
Volume16
Issue number8
DOIs
Publication statusPublished - 29 Nov 2022

Funding

FundersFunder number
the Deutsche ForschungsgemeinschaftES 60/10-1

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