We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 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 -conjecture. We also provide evidence that supports the conjecture in dimension 3 for fields of characteristic .
Marta Pieropan. "On rationally connected varieties over fields of characteristic ." Algebra Number Theory 16 (8) 1811 - 1844, 2022. https://doi.org/10.2140/ant.2022.16.1811