The corestriction op valued division algebras over henselian fields I

When L/F is an unramified extension of Henselian fields, we analyze the underlying division algebra ^CD of the corestriction cor_L/F (D) of a tame division algebra D over L with respect to the unique valuations on ^CD and D extending the valuations on F and L. We show that the value group of CD lies in the value group of D and for the center of residue division algebra, is the normal closure of Z(D) over F and k is an integer depending on which roots of unity lie in F and L.