algebra / Algebraic number theory

Explicit Presentation of the 2-adic Absolute Galois Group

Give an explicit profinite presentation of $\operatorname{Gal}(\overline{\mathbb{Q}}_2 / \mathbb{Q}_2)$. The tame local cases were settled by the early 1980s; the dyadic case was the last one missing. The new presentation has four generators, two word relations and a pro-$2$ condition on the wild generators.

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algebraJul 26, 2026Significance 25/100Registry: lean verified

Explicit Presentation of the 2-adic Absolute Galois Group

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Give an explicit profinite presentation of $\operatorname{Gal}(\overline{\mathbb{Q}}_2 / \mathbb{Q}_2)$. The tame local cases were settled by the early 1980s; the dyadic case was the last one missing. The new presentation has four generators, two word relations and a pro-$2$ condition on the wild generators.

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Give an explicit profinite presentation of $\operatorname{Gal}(\overline{\mathbb{Q}}_2 / \mathbb{Q}_2)$. The tame local cases were settled by the early 1980s; the dyadic case was the last one missing. The new presentation has four generators, two word relations and a pro-$2$ condition on the wild generators.

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