scholarly journals Effective computation of Picard groups and Brauer-Manin obstructions of degree two $$K3$$ surfaces over number fields

2013 ◽  
Vol 62 (1) ◽  
pp. 137-151 ◽  
Author(s):  
Brendan Hassett ◽  
Andrew Kresch ◽  
Yuri Tschinkel
Keyword(s):  
Number Fields ◽  
K3 Surfaces ◽  
Picard Groups

scholarly journals On large Picard groups and the Hasse Principle for curves and K3 surfaces

1996 ◽  
Vol 76 (2) ◽  
pp. 165-189 ◽  
Author(s):  
Daniel Coray ◽  
Constantin Manoil
Keyword(s):  
K3 Surfaces ◽  
Hasse Principle ◽  
Picard Groups

scholarly journals On orders in number fields: Picard groups, ring class fields and applications

2015 ◽  
Vol 58 (8) ◽  
pp. 1627-1638 ◽  
Author(s):  
Chang Lv ◽  
YingPu Deng
Keyword(s):  
Number Fields ◽  
Picard Groups ◽  
Class Fields

scholarly journals Picard Groups on Moduli of K3 Surfaces with Mukai Models

2014 ◽  
Vol 2015 (16) ◽  
pp. 7238-7257 ◽  
Author(s):  
Francois Greer ◽  
Zhiyuan Li ◽  
Zhiyu Tian
Keyword(s):  
K3 Surfaces ◽  
Picard Groups

scholarly journals On the Picard number of K3 surfaces over number fields

2014 ◽  
Vol 8 (1) ◽  
pp. 1-17 ◽  
Author(s):  
François Charles
Keyword(s):  
Number Fields ◽  
K3 Surfaces ◽  
Picard Number

scholarly journals Finiteness theorems for K3 surfaces and abelian varieties of CM type

2018 ◽  
Vol 154 (8) ◽  
pp. 1571-1592 ◽  
Author(s):  
Martin Orr ◽  
Alexei N. Skorobogatov
Keyword(s):  
Abelian Varieties ◽  
Algebraic Closure ◽  
Complex Multiplication ◽  
Uniform Boundedness ◽  
Invariant Subgroup ◽  
Smooth Projective Variety ◽  
Number Fields ◽  
K3 Surfaces ◽  
Isomorphism Classes ◽  
Finiteness Theorems

We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism classes over an algebraic closure of the field of rational numbers. As an application we confirm finiteness conjectures of Shafarevich and Coleman in the CM case. In addition we prove the uniform boundedness of the Galois invariant subgroup of the geometric Brauer group for forms of a smooth projective variety satisfying the integral Mumford–Tate conjecture. When applied to K3 surfaces, this affirms a conjecture of Várilly-Alvarado in the CM case.

K3 SURFACES OVER NUMBER FIELDS ANDl-ADIC REPRESENTATIONS

1989 ◽  
Vol 33 (3) ◽  
pp. 575-595 ◽  
Author(s):  
Sergei G Tankeev
Keyword(s):  
Number Fields ◽  
K3 Surfaces
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