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arXiv · 2402.18418

Flasque quasi-resolutions of algebraic varieties

Mattia Pirani
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Abstract

Flasque resolutions play an important role in understanding birational properties of algebraic tori. For instance, Colliot-Th\'{e}l\`{e}ne and Sansuc have used them to compute $R$-equivalence classes of algebraic tori. We extend this notion to a larger class of algebraic varieties, including homogeneous spaces. This leads to a lower bound on the number of $R$-equivalence classes of homogeneous spaces, which is a slightly stronger version of a theorem of Colliot-Th\'el\`ene and Kunyavskii.

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Mattia Pirani. 2024-02-28. Flasque quasi-resolutions of algebraic varieties. https://arxiv.org/abs/2402.18418

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