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Constructing extensions of number fields with dihedral Galois group

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

In this talk I will prove that given a quadratic extension K of the rational numbers and a prime p, there exist infinitely many Galois extension F/K of degree p such that F/Q is also Galois with dihedral Galois group of order 2p. Moreover, F can be chosen such that arbitrarily many primes ramify in F/K. I will only assume familiarity with Galois theory and some basic theory of number fields (in particular ramification of primes) on the level of a standard undergraduate course. We will use class field theory for the construction but I will state all the results we need.

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

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SS03, William Gates Building. Zoom link: https://cl-cam-ac-uk.zoom.us/j/4361570789?pwd=Nkl2T3ZLaTZwRm05bzRTOUUxY3Q4QT09&from=addon Ross Street Community Centre LR3, CUED

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