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4:00 pm Tuesday, September 28, 2010 Algebraic Geometry Seminar: Transcendental obstructions to weak approximation on general K3 surfacesby
Tony Várilly-Alvarado (Rice) in HB 227- It is well-known that K3 surfaces over number fields need not satisfy the Hasse principle or weak approximation. All known counter-examples to date, however, involve K3 surfaces that are endowed with an elliptic fibration structure; in fact, the fibration is essential to the computation of Brauer classes that reveal obstructions to the Hasse principle and weak approximation. General K3 surfaces, i.e., K3 surfaces with geometric Picard rank one, do not enjoy this kind of structure. I will explain how to construct certain K3 surfaces of geometric Picard rank one, together with a transcendental quaternion algebra that obstructs weak approximation of rational points. This is joint work with Brendan Hassett and Patrick Varilly.
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