Explore: Brauer Groups Of Schemes

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with

basis for his geometric theory of the Brauer group in Bourbaki seminars from 1964–65. There are now several points of access to the basic definitions

Richard Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular

algebraic groups (such as quadratic forms, simple algebras, Severi–Brauer varieties), in the 1930s, before the general theory arrived. The needs of number

étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological

can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced

reductive group schemes over any nonempty scheme S are classified by root data. This statement includes the existence of Chevalley groups as group schemes over

of. They include the Hasse approach of using the Brauer group, cohomological approaches, the explicit methods of Jürgen Neukirch, Michiel Hazewinkel,

years ago. The group Apterygota is not a clade; it is paraphyletic, and not recognized in modern classification schemes. As defined, the group contains two

One of the values of the field is that it also provides new techniques to study objects in commutative algebraic geometry such as Brauer groups. The