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SUMMARY:CFT of IQNF via EC with CM: decomplexifying complex multiplication
  - Marius Leonhardt\, DPMMS
DTSTART:20170427T144000Z
DTEND:20170427T152000Z
UID:TALK72155@talks.cam.ac.uk
CONTACT:Jack Smith
DESCRIPTION:Class Field Theory is concerned with constructing all abelian 
 extensions of a given number field. The general theory culminates in descr
 ibing all the occurring Galois groups\, but curiously it does not give exp
 licit numbers generating those extensions.\n\nFor an imaginary quadratic n
 umber field K\, however\, one can write down the complex numbers belonging
  to its abelian extensions concretely using elliptic curves with complex m
 ultiplication.\n\nIn this talk\, I will explain the "main theorem of compl
 ex multiplication" and sketch its application to the class field theory of
  K. Time permitting\, I will then say a few words about possible generalis
 ations.
LOCATION:MR3\, CMS
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