The Local Reciprocity Map

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• Rachel Newton
• Monday 18 May 2009, 16:00-17:00
• MR13, CMS.

If you have a question about this talk, please contact Anton Evseev.

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

I will describe the cases in which an explicit formula has been found for the local reciprocity map and try to explain why this is difficult in general for totally ramified extensions.

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

This talk is part of the Junior Algebra and Number Theory seminar series.

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