On rationally connected varieties over C1 fields of characteristic 0

Pieropan, Marta

doi:10.2140/ant.2022.16.1811

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

Marta Pieropan

Vol. 16 (2022), No. 8, 1811–1844

DOI: 10.2140/ant.2022.16.1811

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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Keywords

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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

Vol. 16, No. 8, 2022

Marta Pieropan

Abstract

PDF Access Denied

Keywords

Keywords

Mathematical Subject Classification 2010

Milestones

Authors