Question

Can one write a finite extension of local fields as a compositum of fields whose degrees are prime powers?

score 195 · Answer 1 · 2026-03-25 03:02:53

195

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Can one write a finite extension of local fields as a compositum of fields whose degrees are prime powers?

Published on 25 Mar 2026 - 3:02

score 525 · Answer 2 · 2026-03-24 23:46:12

525

Views

Why can we always restrict an Galois representation so that it becomes unramified?

Published on 24 Mar 2026 - 23:46

score 328 · Answer 3 · 2026-03-17 21:02:08

328

Views

Inertia coprime to degree implies Inertia cyclic?

Published on 17 Mar 2026 - 21:02

score 381 · Answer 4 · 2026-03-25 04:42:38

381

Views

Characterization of finite cyclic totally ramified extension of local fields with prime power degree

Published on 25 Mar 2026 - 4:42

score 327 · Answer 5 · 2026-03-25 04:44:18

327

Views

Unramified subextension of the Galois closure of a totaly ramified $p$-adic field

Published on 25 Mar 2026 - 4:44

score 307 · Answer 6 · 2026-03-25 04:36:44

307

Views

Relation between local and global inertia/ramification degrees

Published on 25 Mar 2026 - 4:36

score 115 · Answer 7 · 2026-03-25 04:40:52

115

Views

Image of a character remains the same when restricting to a totally ramified extension

Published on 25 Mar 2026 - 4:40

score 343 · Answer 8 · 2026-03-25 04:40:53

343

Views

Construction of cyclic local field extensions of arbitrary degree and ramification index

Published on 25 Mar 2026 - 4:40

score 382 · Answer 9 · 2026-03-16 21:12:14

382

Views

Ramified Field Extensions

Published on 16 Mar 2026 - 21:12

score 184 · Answer 10 · 2026-03-17 18:46:32

184

Views

Proof of a Lemma for a local field extension with certain properties

Published on 17 Mar 2026 - 18:46

score 352 · Answer 11 · 2018-12-22 21:01:10

352

Views

Computing degrees and ramification indices of some extensions of $\mathbb{Q}_2$

Published on 22 Dec 2018 - 21:01

score 304 · Answer 12 · 2026-03-17 02:19:37

304

Views

Galois Groups in Ramification Theory

Published on 17 Mar 2026 - 2:19

score 82 · Answer 13 · 2019-01-25 15:28:00

82

Views

Is the Inertia quotiented by the first group of ramification $I/G_1\simeq (\mathcal{O}_L/P)^*$?

Published on 25 Jan 2019 - 15:28

score 203 · Answer 14 · 2026-03-24 22:01:58

203

Views

Understanding the $p$-part of the discriminant of a totally real number field with a single prime above $p$

Published on 24 Mar 2026 - 22:01

score 107 · Answer 15 · 2026-03-17 03:11:31

107

Views

Unramified extensions and base change

Published on 17 Mar 2026 - 3:11

List Question

Can one write a finite extension of local fields as a compositum of fields whose degrees are prime powers?

Why can we always restrict an Galois representation so that it becomes unramified?

Inertia coprime to degree implies Inertia cyclic?

Characterization of finite cyclic totally ramified extension of local fields with prime power degree

Unramified subextension of the Galois closure of a totaly ramified $p$-adic field

Relation between local and global inertia/ramification degrees

Image of a character remains the same when restricting to a totally ramified extension

Construction of cyclic local field extensions of arbitrary degree and ramification index

Ramified Field Extensions

Proof of a Lemma for a local field extension with certain properties

Computing degrees and ramification indices of some extensions of $\mathbb{Q}_2$

Galois Groups in Ramification Theory

Is the Inertia quotiented by the first group of ramification $I/G_1\simeq (\mathcal{O}_L/P)^*$?

Understanding the $p$-part of the discriminant of a totally real number field with a single prime above $p$

Unramified extensions and base change

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