The Clemens–Griffiths method over non-closed fields
Olivier Benoist, Olivier Wittenberg
Abstract
We use the Clemens-Griffiths method to construct smooth projective threefolds, over any field k admitting a separable quadratic extension, that are k-unirational and krational but not k-rational. When k = R, we can moreover ensure that their real locus is diffeomorphic to the real locus of a smooth projective R-rational variety and that all their unramified cohomology groups are trivial.
Topics & Concepts
MathematicsPure mathematicsSeparable spaceDiffeomorphismLocus (genetics)Quadratic equationProjective varietyProjective testCohomologyAlgebra over a fieldMathematical analysisGeometryGeneChemistryBiochemistryAlgebraic Geometry and Number TheoryPolynomial and algebraic computationAdvanced Algebra and Geometry