Grothendieck's Brauer group and the Manin obstruction

Grothendieck's Brauer group and the Manin obstruction

Thu, 11/06/2009
12:15 		Frank Gounelas (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Grothendieck's Brauer group and the Manin obstruction
In this talk I will outline the two constructions of the Brauer group Br($ X $) of a scheme $ X $, namely via etale cohomology and Azumaya algebras and briefly describe how one may compute this group using the Hochschild-Serre spectral sequence. In the early '70s Manin observed that one can use the Brauer group of a projective variety $ X/k $ to define an obstruction to the existence of rational points on $ X $. I will discuss this arithmetic application and time permitting, outline an example for $ X $ a K3 surface.