ON THE STRUCTURE OF THE BRAUER GROUP OF FIELDS

Abstract

This paper is devoted to the study of the structure of the Brauer group of an arbitrary field. It is proved that, for any odd prime  different from the characteristic of the field , the subgroup of elements of order in the Brauer group of  is generated by the images of the cyclic algebras under the corestriction map . As a corollary it is shown that is generated by elements whose index is bounded by . A  representation of the -component of the Brauer group by means of generators and relations is obtained, and the specialization homomorphism , where  is a local algebra and  is the residue field, is shown to be surjective. Similar results are obtained in the case . Bibliography: 20 titles.