TY - JOUR
T1 - Galois scaffolds for extraspecial p-extensions in characteristic 0
AU - Keating, Kevin
AU - Schwartz, Paul
N1 - Publisher Copyright:
© 2025 Elsevier Inc.
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 -