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On algebras of exponent two that are trivial in all real closures of their centers. (Russian. English summary) Zbl 1180.16013

Summary: Possible ramification of finite dimensional central simple algebras of exponent two over \(\mathbb{R}(\!(t)\!)(x)\) which are trivial in all real closures of their centers is described. The proof of the local Pfister conjecture is given in cases where either points of ramification are defined by quadratic polynomials or polynomials with roots which are not squares in the corresponding extensions of the field of constants.

MSC:

16K20 Finite-dimensional division rings
16K50 Brauer groups (algebraic aspects)
14H05 Algebraic functions and function fields in algebraic geometry
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