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  "body": "\n## Summary\n\nThe absolute Galois group of a field $K$ is the Galois group of a [[separable closure|JJ91A1V8NQ]] of $K$ over $K$.\nIt contains, as quotients, the Galois groups of all finite Galois extensions of $K$, so it records the whole Galois theory of $K$ at once.\nWith the [[Krull topology|F3GTF5NT4M]] it is a [[profinite group|KA0YDB6QXE]].\n\n## Explanations\n\n### L1 human\n\nInstead of studying one extension of a field at a time, take the largest separable algebraic extension and look at all its symmetries.\nEvery finite Galois extension is a piece of it, and its group is a quotient of the absolute Galois group.\nFor the real numbers, the separable closure is $\\C$, and the absolute Galois group has two elements: the identity and complex conjugation.\nFor $\\Q$, the absolute Galois group is a huge and still mysterious object.\n",
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