Cohomological operations for the Brauer group and Witt kernels of a quartic field extension.

Let be a field, , , a quartic field extension. We investigate the divided power operation on the group . In particular, we show that any element of is a symbol , where , , and is the quadratic trace form associated with the extension . As an application, we obtain certain results on the Stifel-Whitney maps . [ABSTRACT FROM AUTHOR]