Effectivity of Brauer–manin Obstructions on Surfaces
نویسنده
چکیده
We study Brauer–Manin obstructions to the Hasse principle and to weak approximation on algebraic surfaces over number fields. A technique for constructing Azumaya algebra representatives of Brauer group elements is given, and this is applied to the computation of obstructions.
منابع مشابه
Effectivity of Brauer–manin Obstructions
We study Brauer–Manin obstructions to the Hasse principle and to weak approximation, with special regard to effectivity questions.
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Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.
متن کاملTranscendental Obstructions to Weak Approximation on General K3 Surfaces
We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kinds of Brauer classes and cubic fourfolds.
متن کاملOn the Brauer–manin Obstruction for Integral Points
We give examples of Brauer–Manin obstructions to integral points on open subsets of the projective plane.
متن کاملTwo Examples of Brauer–manin Obstruction to Integral Points
We give two examples of Brauer–Manin obstructions to integral points on open subsets of the projective plane.
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تاریخ انتشار 2009