Existence of rational points on smooth projective varieties
From MaRDI portal
Publication:1024257
DOI10.4171/JEMS/159zbMath1183.14032arXiv0712.1782MaRDI QIDQ1024257
Publication date: 16 June 2009
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0712.1782
Decidability (number-theoretic aspects) (11U05) Rational points (14G05) Varieties over global fields (11G35) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20) Global ground fields in algebraic geometry (14G25)
Related Items
Le complémentaire des puissances -ièmes dans un corps de nombres est un ensemble diophantien ⋮ Counting multiplicities in a hypersurface over a finite field ⋮ Curves over every global field violating the local-global principle ⋮ Some aspects of rational points and rational curves ⋮ Non-invariance of the Hasse principle with Brauer-Manin obstruction ⋮ Arithmetic of Châtelet surface bundles revisited ⋮ Arithmetic of Châtelet surfaces under extensions of base fields ⋮ Noninvariance of weak approximation properties under extension of the ground field ⋮ Failure of the Hasse principle for Châtelet surfaces in characteristic 2 ⋮ Degree and the Brauer-Manin obstruction ⋮ Insufficiency of the Brauer-Manin obstruction applied to étale covers ⋮ The arithmetic of certain del Pezzo surfaces and \(K3\) surfaces ⋮ A family of varieties with exactly one pointless rational fiber ⋮ The arithmetic of certain quartic curves ⋮ On the Hasse principle for certain quartic hypersurfaces ⋮ Failure of the Brauer-Manin principle for a simply connected fourfold over a global function field, via orbifold Mordell ⋮ Rational points on conic bundles over elliptic curves
Cites Work
- Hilbert's tenth problem for fields of rational functions over finite fields
- Finiteness theorems for abelian varieties over number fields.
- Logical number theory I. An introduction
- Relating decision and search algorithms for rational points on curves of higher genus
- Hilbert's tenth problem for algebraic function fields of characteristic 2.
- Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
- Complements à un article de Hans Grauert sur la conjecture de Mordell
- Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
- Some remark on rational points
- Hilbert's Tenth Problem for Rings of Algebraic Functions in One Variable Over Fields of Constants of Positive Characteristic
- Hilbert's Tenth Problem for Rational Function Fields in Characteristic 2
- Algebraic families of nonzero elements of Shafarevich-Tate groups
- Some Applications of the Local Uniformization Theorem
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item