List questions from ramification

Published on 13 Apr 2026 - 13:16

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Relationship between wild ramification and restriction in Galois extension

Published on 12 Apr 2026 - 7:03

95

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Condition for an extension to be cyclic – erratum in Mollin's book?

Published on 12 Apr 2026 - 16:12

383

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Ramification indices: what does it mean geometrically that $2$ is the only ramified prime in $\Bbb{Z}[i]$?

Published on 12 Apr 2026 - 11:55

639

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Ramification of a prime ideal in the inertia field

Published on 12 Apr 2026 - 13:25

221

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Why are conductors important?

Published on 10 May 2026 - 19:57

97

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Number of holomorphic map form genus 2 to genus 1 of given a ramification of fixed type

Published on 15 Apr 2026 - 20:58

412

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Cyclic extension of degree $p^2$ ramified at $p$ and outside $p$

Published on 14 Apr 2026 - 7:19

43

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Proof about the closed integral $\mathbb{Z}_p[\zeta_p]$

Published on 26 Mar 2026 - 2:54

52

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Maximal inert extension

Published on 10 May 2026 - 9:37

110

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Construct an extension of a number field of given degree where a given set of prime splits completely

Published on 26 Mar 2026 - 3:01

35

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If $Q \vartriangleleft \Bbb Z[i]$ lies over $(p) \vartriangleleft \Bbb Z$ where $p\in \Bbb Z\setminus\{2\}$, then $e(Q|p) = 1$.

Published on 26 Mar 2026 - 2:57

127

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$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

Published on 25 Mar 2026 - 14:46

326

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What is an Archimedean prime?

Published on 26 Mar 2026 - 2:54

46

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Example of rational jumps in upper ramification filtration

Published on 26 Mar 2026 - 2:54

List Question

Inertia group of compositum of number fields – erratum in Ribenboim's book?

Relationship between wild ramification and restriction in Galois extension

Condition for an extension to be cyclic – erratum in Mollin's book?

Ramification indices: what does it mean geometrically that $2$ is the only ramified prime in $\Bbb{Z}[i]$?

Ramification of a prime ideal in the inertia field

Why are conductors important?

Number of holomorphic map form genus 2 to genus 1 of given a ramification of fixed type

Cyclic extension of degree $p^2$ ramified at $p$ and outside $p$

Proof about the closed integral $\mathbb{Z}_p[\zeta_p]$

Maximal inert extension

Construct an extension of a number field of given degree where a given set of prime splits completely

If $Q \vartriangleleft \Bbb Z[i]$ lies over $(p) \vartriangleleft \Bbb Z$ where $p\in \Bbb Z\setminus\{2\}$, then $e(Q|p) = 1$.

$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

What is an Archimedean prime?

Example of rational jumps in upper ramification filtration

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