On the fibration method for zero-cycles and rational points
From MaRDI portal
Publication:5962628
DOI10.4007/annals.2016.183.1.5zbMath1342.14052arXiv1409.0993OpenAlexW192882128MaRDI QIDQ5962628
Olivier Wittenberg, Yonatan Harpaz
Publication date: 15 February 2016
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.0993
Rational points (14G05) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Fibrations, degenerations in algebraic geometry (14D06) Varieties over global fields (11G35) Brauer groups of schemes (14F22) Global ground fields in algebraic geometry (14G25)
Related Items
Local-global principle for 0-cycles on fibrations over rationally connected bases ⋮ The Hilbert property for arithmetic schemes ⋮ Approximation faible pour les 0-cycles sur un produit de variétés rationnellement connexes ⋮ Enhanced Koszul properties in Galois cohomology ⋮ Une liste de problèmes ⋮ Compatibility of weak approximation for zero-cycles on products of varieties ⋮ Some aspects of rational points and rational curves ⋮ Supersolvable descent for rational points ⋮ ON THE SQUARE-FREE REPRESENTATION FUNCTION OF A NORM FORM AND NILSEQUENCES ⋮ Schinzel hypothesis on average and rational points ⋮ Weak approximation for 0-cycles on a product of elliptic curves ⋮ The fibration method over real function fields ⋮ A local to global principle for higher zero-cycles ⋮ Integral points on conic log K3 surfaces ⋮ Zéro-cycles sur les espaces homogènes et problème de Galois inverse ⋮ Point générique et saut du rang du groupe de Mordell–Weil ⋮ The Schinzel hypothesis for polynomials ⋮ The geometric sieve for quadrics ⋮ Fibrations with few rational points ⋮ The tight approximation property ⋮ Rational points and ramified covers of products of two elliptic curves ⋮ Rational points on fibrations with few non-split fibres ⋮ Four-fold Massey products in Galois cohomology ⋮ Strong Approximation and a Conjecture of Harpaz and Wittenberg ⋮ Arithmetic purity of strong approximation for homogeneous spaces ⋮ Generalized Bockstein maps and Massey products ⋮ Applications of the fibration method to the Brauer–Manin obstruction to the existence of zero-cycles on certain varieties
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Pathologies of the Brauer-Manin obstruction
- Towards the Brauer-Manin obstruction on varieties fibred over the projective line
- The local-global principle for zero cycles on certain fibrations over a curve. I.
- Zero cycles on fibrations over a curve of arbitrary genus
- On the sum of two integral squares in the imaginary quadratic field \(\mathbb Q(\sqrt {-2p})\)
- Cubic polynomials represented by norm forms
- Intersections of two quadrics and pencils of curves of genus 1
- Some observations on motivic cohomology of arithmetic schemes
- Insufficiency of the Brauer-Manin obstruction applied to étale covers
- Finite descent obstructions and rational points on curves
- La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)
- On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch
- Zero-cycles on rational surfaces over number fields
- Beyond the Manin obstruction. -- Appendix A by S. Siksek: 4-descent. -- Appendix B: The Grothendieck spectral sequence and the truncation functor
- Fibration method and Manin obstruction
- Rationally connected varieties over finite fields
- Rational solutions of certain equations involving norms
- The Brauer group of torsors and its arithmetic applications.
- The arithmetic of the Chow group of zero-cycles
- Singular homology of abstract algebraic varieties
- Rational points on pencils of conics and quadrics with many degenerate fibres
- Universal torsors and values of quadratic polynomials represented by norms
- The local-global exact sequence for Chow groups of zero-cycles
- Unramified cohomology and the entire Hodge conjecture
- Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
- Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
- Rational surfaces over perfect fields
- Spécialisation du foncteur de Picard
- Séminaire de géométrie algébrique du Bois Marie 1960/61 (SGA 1), dirigé par Alexander Grothendieck. Augmenté de deux exposés de M. Raynaud. Revêtements étales et groupe fondamental. Exposés I à XIII. (Seminar on algebraic geometry at Bois Marie 1960/61 (SGA 1), directed by Alexander Grothendieck. Enlarged by two reports of M. Raynaud. Ètale coverings and fundamental group)
- Abelian varieties over \(p\)-adic ground fields
- A NOTE ON A THEOREM OF HEATH-BROWN AND SKOROBOGATOV
- Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus de l'espace projectif
- On the equation N K /k (Ξ)=P (t )
- Descent on toric fibrations
- Arithmetic on certain quadric bundles of relative dimension 2. I.
- Remarks on Correspondences and Algebraic Cycles
- Sur le principe de Hasse et l'approximation faible, et sur une hypothèse de Schinzel
- Higher-dimensional analogs of Châtelet surfaces
- Norm forms for arbitrary number fields as products of linear polynomials
- Topics in Diophantine Equations
- Index of varieties over Henselian fields and Euler characteristic of coherent sheaves
- Some remark on rational points
- A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
- Rational points on cubic hypersurfaces that split off a form. With an appendix by J.-L. Colliot-Thélène
- Zéro-cycles de degré 1 sur les solides de Poonen
- Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres.
- Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.
- Rational Points on Pencils of Conics and on Pencils of Quadrics
- Flèches de spécialisations en cohomologie étale et applications arithmétiques
- Obstruction de Brauer-Manin pour les zéro-cycles sur des fibrations en variétés de Severi-Brauer
- On the representation of primes by cubic polynomials in two variables
- THE BRAUER–MANIN OBSTRUCTION FOR ZERO-CYCLES ON SEVERI–BRAUER FIBRATIONS OVER CURVES
- Descent on fibrations over P1k revisited
- ON THE SQUARE-FREE REPRESENTATION FUNCTION OF A NORM FORM AND NILSEQUENCES
- Algebraic families of nonzero elements of Shafarevich-Tate groups
- Principe local-global pour les zéro-cycles sur les surfaces réglées
- Descent on fibrations over the projective line
- Families of rationally connected varieties
- The Brauer-Manin obstructions for homogeneous spaces with connected or abelian stabilizer.
- Strong approximation for the total space of certain quadric fibrations
- Good reduction of the Brauer–Manin obstruction
- Arithmetic of 0-cycles on varieties defined over number fields
- Local-global principle for certain biquadratic normic bundles
- The Hardy–Littlewood conjecture and rational points
- Astuce de Salberger et Zéro-cycles Sur Certaines Fibrations
- Principes locaux-globaux pour certaines fibrations en torseurs sous un tore
- Categories and Sheaves
- Number of Points of Varieties in Finite Fields
- Higher-dimensional algebraic geometry
