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Arithmetic of K3 Surfaces (Q4645320)

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scientific article; zbMATH DE number 6999627

Language	Label	Description	Also known as
English	Arithmetic of K3 Surfaces	scientific article; zbMATH DE number 6999627

Statements

scholarly article

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Arithmetic of K3 Surfaces (English)

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Anthony Várilly-Alvarado

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Geometry Over Nonclosed Fields

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publication date

10 January 2019

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zbMATH Keywords

moduli spaces

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number fields

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central simple algebras

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Kummer surfaces

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\(K3\) surfaces

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Hasse principle

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-319-49763-1_7

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Level structures on abelian varieties, Kodaira dimensions, and Lang's conjecture

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Insufficiency of the Brauer-Manin obstruction for rational points on Enriques surfaces

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The Brauer–Manin obstruction on a general diagonal quartic surface

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On the Torelli problem for kählerian $K-3$ surfaces

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Diophantine Equations with Special Reference To Elliptic Curves

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The Tate conjecture for \(K3\) surfaces over finite fields

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On the Picard number of \(K3\) surfaces over number fields

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Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for \(K3\) surfaces, and the Tate conjecture

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The arithmetic of rational varieties

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La descente sur les variétés rationnelles. II. (The descent on rational varieties. II)

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Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points

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Enriques surfaces. I

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Variation of Néron–Severi Ranks of Reductions of K3 Surfaces

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K3 Surfaces of Picard Rank One and Degree Two

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On the computation of the Picard group for <i>K</i>3 surfaces

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The Picard group of a \(K3\) surface and its reduction modulo \(p\)

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Kummer surfaces and the computation of the Picard group

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Experiments with the transcendental Brauer-Manin obstruction

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Effective bounds for Brauer groups of Kummer surfaces over number fields

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The Kodaira dimension of the moduli of \(K3\) surfaces

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Moduli of K3 Surfaces and Irreducible Symplectic Manifolds

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Hasse principle for Kummer varieties

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Effective computation of Picard groups and Brauer-Manin obstructions of degree two \(K3\) surfaces over number fields

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Failure of the Hasse principle on general surfaces

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Transcendental obstructions to weak approximation on general \(K3\) surfaces

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Derived equivalent surfaces and abelian varieties, and their zeta functions

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Diagonal quartic surfaces and transcendental elements of the Brauer group

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Odd order Brauer-Manin obstruction on diagonal quartic surfaces

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On the Brauer group of diagonal quartic surfaces

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RANK 2 SHEAVES ON K3 SURFACES: A SPECIAL CONSTRUCTION

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Unramified Brauer Classes on Cyclic Covers of the Projective Plane

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Torsion points on elliptic curves and \(q\)-coefficients of modular forms

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On the Albanese variety of the moduli space of polarized K3 surfaces

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On the arithmetic of del Pezzo surfaces of degree 2

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Effectivity of Brauer-Manin obstructions

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Effectivity of Brauer-Manin obstructions on surfaces

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Elliptic <i>K</i>3 Surfaces with Geometric Mordell–Weil Rank 15

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Fourier-Mukai partners of K3 surfaces in positive characteristic

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On the Brauer group of a surface

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Fano varieties of cubic fourfolds containing a plane

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The Tate conjecture for \(K3\) surfaces in odd characteristic

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Supersingular \(K3\) surfaces for large primes. With an Appendix by Andrew Snowden.

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Néron-Severi groups under specialization

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Modular curves and the Eisenstein ideal

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Brauer Groups on K3 Surfaces and Arithmetic Applications

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Bounds for the torsion of elliptic curves over number fields

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On a conjecture of Artin and Tate

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Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface

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Transcendental Brauer groups of products of CM elliptic curves

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INTEGRAL SYMMETRIC BILINEAR FORMS AND SOME OF THEIR APPLICATIONS

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The Tate conjecture for ordinary K 3 surfaces over finite fields

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Tate's conjecture for \(K3\) surfaces of finite height

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Diophantine equations and modular forms

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Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$

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Computing Néron–Severi groups and cycle class groups

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Einige im Kleinen überall lösbare, im Großen unlösbare diophantische Gleichungen.

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Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties

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Topological methods for complex-analytic Brauer groups

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Arithmetic of \(K3\) surfaces

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Two Lectures on the Arithmetic of K3 Surfaces

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Algebraic geometry and analytic geometry

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The Arithmetic of Elliptic Curves

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Every K 3 surface is Kähler

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2-descent on elliptic curves and rational points on certain Kummer surfaces

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A finiteness theorem for the Brauer group of abelian varieties and 𝐾3 surfaces

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The Brauer group of Kummer surfaces and torsion of elliptic curves

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Kodaira dimension of moduli of special cubic fourfolds

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Complete intersections with middle Picard number 1 defined over \({\mathbb{Q}}\)

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Applications of the Kaehler-Einstein-Calabi-Yau metric to moduli of K3 surfaces

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Some remarks on Brauer groups of \(K3\) surfaces

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\(K3\) surfaces with Picard number one and infinitely many rational points

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Weak approximation on del Pezzo surfaces of degree 1

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Arithmetic of Del Pezzo surfaces

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Failure of the Hasse principle for Enriques surfaces

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Théorème de Torelli pour les cubiques de \({\mathbb{P}}^ 5\). (Torelli theorem for the cubics of \({\mathbb{P}}^ 5)\)

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Transcendental Brauer-Manin obstruction on a pencil of elliptic curves

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Hodge groups of K3 surfaces.

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-49763-1_7

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:4645320

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