THE CORESTRICTION OF CENTRAL SIMPLE ALGEBRAS WITH DUBROVIN VALUATION RINGS

We analyze the corestriction CO Gamma(L/F)(S) of a central simple algebra S over L with respect to a Dubrovin valuation ring A (resp. B-i) of CO Gamma(L/F)(S) (resp. S) extending V on F (resp. W-i on L) where L is a finite separable extension of F and the W-i are the extensions of V to L for 1 less than or equal to i less than or equal to k. Under the suitable conditions, we show that for the value group, Gamma(A) subset of or equal to [GRAPHICS] and for the center of residue ring, Z(($) over bar A) subset of or equal to [GRAPHICS] where N(Z(($$$) over bar B-i)/($) over bar F is the normal closure of Z(($$$) over bar B-i)/($) over bar F and m(i) is an integer depending on which roots of unity lie in F and L.