Abstract
Around 1989, Manin initiated a program to understand the asymptotic behaviour of rational points of bounded height on Fano varieties. This program led to the search of new methods to estimate the number of points of bounded height on various classes of varieties. Methods based on harmonic analysis were successful for compactifications of homogeneous spaces. However, they do not apply to other types of varieties. Universal torsors, introduced by Colliot-Thélène and Sansuc in connection with the Hasse principle and weak approximation, turned out to be a useful tool in the treatment of other varieties. The aim of this short survey is to describe the use of torsors in various representative examples.
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Peyre, E. (2004). Counting Points On Varieties Using Universal Torsors. In: Poonen, B., Tschinkel, Y. (eds) Arithmetic of Higher-Dimensional Algebraic Varieties. Progress in Mathematics, vol 226. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8170-8_4
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DOI: https://doi.org/10.1007/978-0-8176-8170-8_4
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