The Local Reciprocity Map
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 Rachel Newton
 Monday 18 May 2009, 16:0017:00
 MR13, CMS.
If you have a question about this talk, please contact Anton Evseev.
I will take the oldfashioned approach and develop a definition of the
local reciprocity map (for finite abelian extensions of the padics) 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/Logic/Number Theory seminar series.
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