A finiteness theorem for the Brauer group of abelian varieties and 𝐾3 surfaces
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Publication:3518212
DOI10.1090/S1056-3911-07-00471-7zbMath1157.14008arXivmath/0605351OpenAlexW1969583401MaRDI QIDQ3518212
Alexei N. Skorobogatov, Yuri G. Zarhin
Publication date: 7 August 2008
Published in: Journal of Algebraic Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0605351
(K3) surfaces and Enriques surfaces (14J28) Arithmetic ground fields for abelian varieties (14K15) Brauer groups of schemes (14F22)
Related Items (39)
Diagonal quartic surfaces and transcendental elements of the Brauer group ⋮ Cohomology and the Brauer groups of diagonal surfaces ⋮ Finiteness of Brauer groups of K3 surfaces in characteristic 2 ⋮ Invariant Brauer group of an abelian variety ⋮ Principe local-global pour les zéro-cycles sur certaines fibrations au-dessus de l'espace projectif ⋮ Divisibility results for zero-cycles ⋮ Explicit uniform bounds for Brauer groups of singular \(K3\) surfaces ⋮ Evaluating the wild Brauer group ⋮ Compatibility of weak approximation for zero-cycles on products of varieties ⋮ Boundedness of the p-primary torsion of the Brauer group of an abelian variety ⋮ On the Brauer group of an arithmetic model of strictly complete intersection in a hyperkähler variety over a number field ⋮ Effective computation of Picard groups and Brauer-Manin obstructions of degree two \(K3\) surfaces over number fields ⋮ Weak approximation for 0-cycles on a product of elliptic curves ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Degree and the Brauer-Manin obstruction ⋮ Bounds on the torsion subgroups of Néron–Severi groups ⋮ Odd order Brauer-Manin obstruction on diagonal quartic surfaces ⋮ Cohomology of algebraic varieties over the maximal cyclotomic extension of a global field ⋮ Point générique et saut du rang du groupe de Mordell–Weil ⋮ ABELIAN -DIVISION FIELDS OF ELLIPTIC CURVES AND BRAUER GROUPS OF PRODUCT KUMMER & ABELIAN SURFACES ⋮ Arithmetic of K3 Surfaces ⋮ Abelian varieties over fields of finite characteristic ⋮ Good reduction of the Brauer–Manin obstruction ⋮ Homomorphisms of abelian varieties over geometric fields of finite characteristic ⋮ Galois descent for higher Brauer groups ⋮ Finiteness theorems for K3 surfaces and abelian varieties of CM type ⋮ Complex multiplication and Brauer groups of \(K3\) surfaces ⋮ Transcendental Brauer groups of products of CM elliptic curves ⋮ On cubic torsors, biextensions and Severi-Brauer varieties over abelian varieties ⋮ On a torsion analogue of the weight-monodromy conjecture ⋮ Descent obstruction is equivalent to étale Brauer-Manin obstruction ⋮ A uniform bound on the Brauer groups of certain log $K3$ surfaces ⋮ Ordinary reduction of K3 surfaces ⋮ The Brauer–Manin obstruction on Kummer varieties and ranks of twists of abelian varieties ⋮ Failure of the Hasse principle on general surfaces ⋮ Linear relations and arithmetic on abelian schemes ⋮ On the finiteness of the Brauer group of an arithmetic scheme ⋮ On uniformity conjectures for abelian varieties and K3 surfaces ⋮ Applications of the fibration method to the Brauer–Manin obstruction to the existence of zero-cycles on certain varieties
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