On the residue fields of Henselian valued stable fields

Abstract: Let 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 properly includes its subgroup . The paper shows that if is the residue field of 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 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 . [Copyright &y& Elsevier]