Problems
- No direct description is known for the absolute Galois group of the rational numbers. In this case, it follows from Belyi's theorem that the absolute Galois group has a faithful action on the dessins d'enfants of Grothendieck (maps on surfaces), enabling us to "see" the Galois theory of algebraic number fields.
- Let K be the maximal abelian extension of the rational numbers. Then Shafarevich's conjecture asserts that the absolute Galois group of K is a free profinite group.
Read more about this topic: Absolute Galois Group
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