Algebraic Geometry Seminar

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The Brauer Group and the Brauer-Manin Obstruction for K3 Surfaces

Speaker: Alexei Skorobogatov, Imperial College, London

Location: Warren Weaver Hall 201

Date: Tuesday, April 8, 2014, 3:30 p.m.

Synopsis:

A consequence of the recent proof of the Tate conjecture for K3 surfaces is the finiteness of the prime-to-p torsion subgroup of the transcendental Brauer group of K3 surfaces in odd characteristic p. This is a joint work with Yuri Zarhin. I will also discuss how in some cases one can compute the Brauer group, construct Brauer classes and calculate the Brauer-Manin obstruction. Examples will be mostly taken from a joint work with Evis Ieronymou on diagonal quartic surfaces over the rational numbers.