Table of Contents

Generic splitting fields.- Crossed products over graded local rings.- Brauer group and diophantine geometry: A cohomological approach.- Brauer groups and class groups for a Krull domain.- Some remarks on Brauer groups of Krull domains.- Generic algebras.- Splitting rings for azumaya quaternion algebras.- Sur les decompositions des algebres a division en produit tensoriel d'algebres cycliques.- Local structure of maximal orders on surfaces.- Left ideals in maximal orders.- Brauer-Severi varieties.- On the Brauer group of surfaces and subrings of k[x,y].- The Brauer groups in complex geometry.- When is Br(X)=Br?(X)?.- Quaternionic modules over—2 (?).- The Brauer group of a quasi affine-scheme.- A check list on Brauer groups.