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Adrien Douady () and Régine Douady
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Adrien Douady: Université Paris-Sud Orsay
Régine Douady: Université Paris Denis-Diderot

Chapter 7 in Algebra and Galois Theories, 2020, pp 407-447 from Springer

Abstract: Abstract The Galois group $${\mathbb G}= \mathrm{Aut}_{\mathbb Q}(\overline{{\mathbb Q}})$$ , where $$\overline{{\mathbb Q}}$$ is an algebraic closure of $${\mathbb Q}$$ , let us say in $${\mathbb C}$$ , fascinates arithmeticians. This profinite group is hard to grasp. It certainly embeds in the product of $${\mathfrak S}(P^{-1}(0))$$ , as P runs through the set of irreducible polynomials of $${\mathbb Z}[X]$$ , but this set is itself not easy to understand if only because there is no natural way of numbering the roots of a polynomial.

Date: 2020
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DOI: 10.1007/978-3-030-32796-5_7

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