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Une liste de problèmes

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Mathematics Going Forward

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2313))

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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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Authors and Affiliations

  1. CNRS, Laboratoire de mathématiques d’Orsay, Université Paris-Saclay, Orsay, France

    Jean-Louis Colliot-Thélène

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  1. Jean-Louis Colliot-Thélène
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Correspondence to Jean-Louis Colliot-Thélène .

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  1. CMLA, École Normale Supérieure, Cachan CX, France

    Jean-Michel Morel

  2. Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013, Paris, France

    Bernard Teissier

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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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