Galois scaffolds for extraspecial p-extensions in characteristic 0

Kevin Keating; Paul Schwartz

doi:10.1016/j.jnt.2025.05.005

Galois scaffolds for extraspecial p-extensions in characteristic 0

Kevin Keating
, Paul Schwartz

Department of Mathematical Sciences

University of Florida

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a local field of characteristic 0 with residue characteristic p>2. Let G be an extraspecial p-group and let L/K be a totally ramified G-extension. In this paper we find sufficient conditions for L/K to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers O_L to be free of rank 1 over its associated order A_L/K, and to stricter conditions which imply that A_L/K is a Hopf order in the group ring K[G].

Original language	English
Pages (from-to)	893-923
Number of pages	31
Journal	Journal of Number Theory
Volume	278
DOIs	https://doi.org/10.1016/j.jnt.2025.05.005
State	Published - Jan 2026

Keywords

Extraspecial p-groups
Galois module structure
Galois scaffolds
Hopf algebras

Access to Document

10.1016/j.jnt.2025.05.005

Cite this

@article{74c14d795b0542909fc9dda1e4434ed1,

title = "Galois scaffolds for extraspecial p-extensions in characteristic 0",

abstract = "Let K be a local field of characteristic 0 with residue characteristic p>2. Let G be an extraspecial p-group and let L/K be a totally ramified G-extension. In this paper we find sufficient conditions for L/K to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers OL to be free of rank 1 over its associated order AL/K, and to stricter conditions which imply that AL/K is a Hopf order in the group ring K[G].",

keywords = "Extraspecial p-groups, Galois module structure, Galois scaffolds, Hopf algebras",

author = "Kevin Keating and Paul Schwartz",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2026",

month = jan,

doi = "10.1016/j.jnt.2025.05.005",

language = "English",

volume = "278",

pages = "893--923",

}

TY - JOUR

T1 - Galois scaffolds for extraspecial p-extensions in characteristic 0

AU - Keating, Kevin

AU - Schwartz, Paul

PY - 2026/1

Y1 - 2026/1

N2 - Let K be a local field of characteristic 0 with residue characteristic p>2. Let G be an extraspecial p-group and let L/K be a totally ramified G-extension. In this paper we find sufficient conditions for L/K to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers OL to be free of rank 1 over its associated order AL/K, and to stricter conditions which imply that AL/K is a Hopf order in the group ring K[G].

AB - Let K be a local field of characteristic 0 with residue characteristic p>2. Let G be an extraspecial p-group and let L/K be a totally ramified G-extension. In this paper we find sufficient conditions for L/K to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers OL to be free of rank 1 over its associated order AL/K, and to stricter conditions which imply that AL/K is a Hopf order in the group ring K[G].

KW - Extraspecial p-groups

KW - Galois module structure

KW - Galois scaffolds

KW - Hopf algebras

UR - https://www.scopus.com/pages/publications/105008936373

UR - https://www.scopus.com/pages/publications/105008936373#tab=citedBy

U2 - 10.1016/j.jnt.2025.05.005

DO - 10.1016/j.jnt.2025.05.005

M3 - Article

AN - SCOPUS:105008936373

SN - 0022-314X

VL - 278

SP - 893

EP - 923

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Galois scaffolds for extraspecial p-extensions in characteristic 0

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this