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

Marta Pieropan

Vol. 16 (2022), No. 8, 1811–1844
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.

Keywords
rationally connected varieties, rational points, Fano varieties, $C_1$ fields
Mathematical Subject Classification 2010
Primary: 14M22
Secondary: 14G05, 14J45
Milestones
Received: 17 September 2019
Revised: 5 August 2021
Accepted: 10 October 2021
Published: 29 November 2022
Authors
Marta Pieropan
Mathematical Institute
Utrecht University
Utrecht
Netherlands
EPFL
Lausanne
Switzerland