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Embedding problems and equivalence of quadratic forms
If the obstruction to a Galois theoretical embedding problem with kernel of order $2$ is the product of two quaternion classes, the criterion for solvability can be reformulated as an equivalence of quadratic forms. In some cases the solutions to the embedding problem can be constructed directly from a matrix expressing this equivalence.doi:10.7146/math.scand.a-14327 fatcat:m4cewtgedzbypmcabczc4bqqtq