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arXiv · 2505.21477

Vari\'et\'es r\'eelles connexes non stablement rationnelles

Jean-Louis Colliot-Thélène·Alena Pirutka·Federico Scavia
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Abstract

Let $R$ be the field of real Puiseux series. It is a real closed field. We construct the first examples of smooth intersections of two quadrics in $\mathbb{P}_R^5$ and smooth cubic hypersurfaces in $\mathbb{P}_R^4$ which are not stably rational but for which the space $X(R)$ of $R$-points is semi-algebraically connected. The question of constructing such examples over the field of real numbers $\mathbb{R}$ remains open.

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Jean-Louis Colliot-Thélène, Alena Pirutka, Federico Scavia. 2025-05-27. Vari\'et\'es r\'eelles connexes non stablement rationnelles. https://arxiv.org/abs/2505.21477

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