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Explicit local reciprocity for tame extensions

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I will take the old-fashioned approach and develop a definition of the local reciprocity map using cyclic algebras. Along the way, I will introduce the Brauer group (which classifies central simple algebras) and define the Hasse invariant.

I will consider a tamely ramified abelian extension of local fields of degree n, without assuming the presence of the n th roots of unity in the base field. I will give an explicit formula which computes the local reciprocity map in this situation.

This talk should be accessible to anyone who has encountered extensions of local fields.

This talk is part of the Number Theory Seminar series.

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