Question

Ramification index and inertia degree same for all the primes, then is the extension Galois

score 402 · Answer 1 · 2026-04-15 19:14:46

402

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Ramification index and inertia degree same for all the primes, then is the extension Galois

Published on 15 Apr 2026 - 19:14

score 621 · Answer 2 · 2026-04-14 23:23:40

621

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Ramification groups

Published on 14 Apr 2026 - 23:23

score 527 · Answer 3 · 2026-04-09 10:49:43

527

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Doubt about higher ramification groups

Published on 09 Apr 2026 - 10:49

score 160 · Answer 4 · 2026-04-12 06:58:24

160

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Is it correct ? $p\in\mathbb{Z}$ tamely ramified in $K\implies[K:\mathbb{Q}]$ is coprime to $p$

Published on 12 Apr 2026 - 6:58

score 66 · Answer 5 · 2026-04-14 23:49:19

66

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ramification of a rational prime in conjugate fields

Published on 14 Apr 2026 - 23:49

score 448 · Answer 6 · 2026-04-09 05:54:16

448

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How to compute higher ramification groups?

Published on 09 Apr 2026 - 5:54

score 114 · Answer 7 · 2026-04-14 05:02:49

114

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Looking for some numerical examples of decomposition groups and ramification groups

Published on 14 Apr 2026 - 5:02

score 260 · Answer 8 · 2026-04-16 02:06:33

260

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Looking for examples of abelian extensions of $\mathbb{Q}$ satisfying a certain condition

Published on 16 Apr 2026 - 2:06

score 46 · Answer 9 · 2026-04-15 12:35:52

46

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Given a number field $K$, is there a number field $L$ containing $K$ such that all prime ideals of $K$ are unramified in $L$?

Published on 15 Apr 2026 - 12:35

score 1.6k · Answer 10 · 2026-04-08 17:45:55

1.6k

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Trying to understand the definition of Hilbert Class Field

Published on 08 Apr 2026 - 17:45

score 679 · Answer 11 · 2026-04-09 06:07:44

679

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A proof of Minkowski's ramification theorem without the use of geometry of numbers

Published on 09 Apr 2026 - 6:07

score 509 · Answer 12 · 2026-04-11 15:26:37

509

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Ramification in infinite Galois extensions

Published on 11 Apr 2026 - 15:26

score 279 · Answer 13 · 2026-04-11 17:27:08

279

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A doubt about ramification in cyclotomic fields

Published on 11 Apr 2026 - 17:27

score 393 · Answer 14 · 2026-04-16 16:02:11

393

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Prove that a polynomial with integer coefficients splits into linear factors modulo infinite number of primes

Published on 16 Apr 2026 - 16:02

score 1.2k · Answer 15 · 2026-04-13 20:36:38

1.2k

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wildly ramified extensions and $p$-power roots of unity

Published on 13 Apr 2026 - 20:36

List Question

Ramification index and inertia degree same for all the primes, then is the extension Galois

Ramification groups

Doubt about higher ramification groups

Is it correct ? $p\in\mathbb{Z}$ tamely ramified in $K\implies[K:\mathbb{Q}]$ is coprime to $p$

ramification of a rational prime in conjugate fields

How to compute higher ramification groups?

Looking for some numerical examples of decomposition groups and ramification groups

Looking for examples of abelian extensions of $\mathbb{Q}$ satisfying a certain condition

Given a number field $K$, is there a number field $L$ containing $K$ such that all prime ideals of $K$ are unramified in $L$?

Trying to understand the definition of Hilbert Class Field

A proof of Minkowski's ramification theorem without the use of geometry of numbers

Ramification in infinite Galois extensions

A doubt about ramification in cyclotomic fields

Prove that a polynomial with integer coefficients splits into linear factors modulo infinite number of primes

wildly ramified extensions and $p$-power roots of unity

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