Abstract
I collect a number of open problems on the arithmetic—in a broad sense—of rationally connected varieties, such as Fano varieties or homogeneous spaces of connected linear algebraic groups. Most of these problems have been with us for a long time. In one direction, one is interested in problems of Lüroth type: when are such varieties birational to projective space? In another direction, over a ground field which is not algebraically closed, and foremost over a number field, one is interested in the existence and density of rational points on such varieties. Analogous questions on zero-cycles are also reviewed.
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Colliot-Thélène, JL. (2023). Une liste de problèmes. In: Morel, JM., Teissier, B. (eds) Mathematics Going Forward . Lecture Notes in Mathematics, vol 2313. Springer, Cham. https://doi.org/10.1007/978-3-031-12244-6_2
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