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Results tagged with nt.number-theory
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user 126439
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
17
votes
Accepted
Cyclic cubic extensions and Kummer theory
It's just the map
$$x \mapsto y = \frac{x}{x^{\sigma}},$$
where the corresponding degree three extension of $\mathbb{Q}$ is the degree three subfield of $k(y^{1/3})$. The point is that it is obviou …
15
votes
Accepted
Centraliser of an absolute Galois group
For an extension $L/\mathbf{Q}_p$, let $G_L$ denote the absolute Galois group $\mathrm{Gal}(\overline{L}/L)$.
If $\sigma \in G_{\mathbf{Q}_p}$ acts centrally on $G_K$, then it also acts centrally on …