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We introduce cyclotomic polynomials, and use Frobenius automorphisms to show they are irreducible. We give two applications of them: we prove a special case of Dirichlet’s theorem on primes in arithmetic progressions, and we show that any finite abelian group is the Galois group of a finite extension of the rational numbers ℚ.
This video is part of a lecture course by Richard Borcherds from 2020-21.