Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different

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Let K be a finite extension of ₚ, let L/K be a finite abelian Galois extension of odd degree and let ₗ be the valuation ring of L. We define Aₗ/ₖ to be the unique fractional ₗ-ideal with square equal to the inverse different of L/K. For p an odd prime and L/ₚ contained in certain cyclotomic extensions, Erez has described integral normal bases for Aₗ/ₚ that are self-dual with respect to the trace form. Assuming K/ₚ to be unramified we generate odd abelian weakly ramified extensions of K using Lubin-Tate formal groups. We then use Dwork's exponential power series to explicitly construct self-dual integral normal bases for the square-root of the inverse different in these extensions.