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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 ${C}_{1}$-conjecture. We also provide evidence that supports the conjecture in dimension 3 for ${C}_{1}$ fields of characteristic 0.

##### Keywords
rationally connected varieties, rational points, Fano varieties, $C_1$ fields
##### Mathematical Subject Classification 2010
Primary: 14M22
Secondary: 14G05, 14J45