Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588417 | Journal of Algebra | 2008 | 34 Pages |
Abstract
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 .
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