Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces
Ronald van Luijk (2011)
Acta Arithmetica
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Displaying similar documents to “On diagonal cubic surfaces.”
Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces
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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...