 Home

Codex Wiki

Mathematics

Area of mathematics

Arithmetic

Non-Archimedean analysis

Absolute value on a field

Extension of an absolute value

Local factorization and extended absolute values

Completion of a number field at a prime ideal

For a prime $\mathfrak q$ of a finite separable extension $L/K$ above $\mathfrak p$, completion preserves the <ramification index> and <residue-field extension>:
$$
e(L_{\mathfrak q}/K_{\mathfrak p})=e_{\mathfrak q/\mathfrak p},
\qquad
k_{L_{\mathfrak q}}=k_{\mathfrak q}.
$$

Completion preserves ramification and residue data

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 123 / 1 / ii / Solution

Completion preserves ramification and residue data

 Ancestors (9)

 Incoming links (1)

 Discussion (0)

 Articles by others on the same topic (0)

Completion preserves ramification and residue data

 Ancestors (9)

 Incoming links (1)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)