Variétés réelles connexes non stablement rationnelles

2025/05/27 by Jean-Louis Colliot-Thélène, Alena Pirutka, Colliot-Thélène, Jean-Louis +3
Computer Science · Mathematics · #14E08 (Primary) 14M20 #14F20 (Secondary) #14P10 #14P25 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.21477

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℙ_R⁵ and smooth cubic hypersurfaces in ℙ_R⁴ 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 ℝ remains open.

Citations

• ON THE RATIONALITY OF SOME REAL THREEFOLDS
• Unramified cohomology, algebraic cycles and rationality
• Rationality of even-dimensional intersections of two real quadrics
• Intermediate Jacobians and rationality over arbitrary fields
• Hypersurfaces quartiques de dimension 3 : non rationalité stable
• Universal unramified cohomology of cubic fourfolds containing a plane

Related

• Non rationalité stable d'hypersurfaces cubiques sur des corps non algébriquement clos
• Non rationalité stable sur les corps quelconques
• Rationality of even-dimensional intersections of two real quadrics
• A Stably Irrational (2,3)-Complete Intersection Fourfold over ℚ
• Hypersurfaces quartiques de dimension 3 : non rationalité stable