Fields for which the projective schur subgroup is the whole Brauer group |
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Authors: | Eli Aljadeff Jack Sonn |
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Institution: | (1) Department of Mathematics, Technion, Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | LetBr(K) denote the Brauer group of a fieldK andPS(K) the projective Schur subgroup.
1. LetK be a finitely generated infinite field. ThenPS(K)=Br(K) if and only ifK is a global field.
2.|LetK be a finitely generated infinite field, and letK((t)) denote the field of formal power series int overK. ThenPS(K((t)))=Br(K((t))) if and only ifK=ℚ. |
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