2019/09/27 by Olivier Benoist, Olivier Wittenberg, Benoist, Olivier +1 · 4 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics
paper · doi:10.48550/arxiv.1909.12668
openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational threefolds over arbitrary, not necessarily perfect, fields. As a consequence, we obtain the first examples of smooth projective varieties over a field k which have a k-point, and are rational over a purely inseparable field extension of k, but not over k.