CFT of IQNF via EC with CM: decomplexifying complex multiplication

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• Marius Leonhardt, DPMMS
• Thursday 27 April 2017, 15:40-16:20
• MR3, CMS.

If you have a question about this talk, please contact Jack Smith.

Class Field Theory is concerned with constructing all abelian extensions of a given number field. The general theory culminates in describing all the occurring Galois groups, but curiously it does not give explicit numbers generating those extensions.

For an imaginary quadratic number field K, however, one can write down the complex numbers belonging to its abelian extensions concretely using elliptic curves with complex multiplication.

In this talk, I will explain the “main theorem of complex multiplication” and sketch its application to the class field theory of K. Time permitting, I will then say a few words about possible generalisations.

This talk is part of the DPMMS PhD student colloquium series.

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