On the residue fields of Henselian valued stable fields

Let (K,v) be a Henselian valued field satisfying the following conditions, for a given prime number p: (i) central division K-algebras of (finite) p-primary dimensions have Schur indices equal to their exponents; (ii) the value group v(K) properly includes its subgroup pv(K). The paper shows that if is the residue field of (K,v) and is an intermediate field of the maximal p-extension , then the natural homomorphism of Brauer groups maps surjectively the p-component on . It proves that is divisible, if p>2 or is a nonreal field, and that is of order 2 when is formally real. We also obtain that embeds as a -subalgebra in a central division -algebra if and only if the degree divides the index of .