Brauer Group - General Theory

General Theory

For an arbitrary field K, the Brauer group may be expressed in terms of Galois cohomology as follows:

Here, Ks is the separable closure of K, which coincides with the algebraic closure when K is a perfect field.

A generalisation of the Brauer group to the case of commutative rings by M. Auslander and O. Goldman, and more generally to schemes, was introduced by Alexander Grothendieck. In their approach, central simple algebras over a field are replaced with Azumaya algebras.

Read more about this topic:  Brauer Group

Famous quotes containing the words general and/or theory:

    At that,
    his small size,
    keen eyes,
    serviceable beak
    and general truculence
    assure his survival—
    William Carlos Williams (1883–1963)

    Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.
    —H.L. (Henry Lewis)