Galois scaffolds for extraspecial p-extensions in characteristic 0

2024/07/24 by Keating, Kevin, Schwartz, Paul
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.17355

Abstract

Let K be a local field of characteristic 0 with residue characteristic p. 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 \mathfrakO_L to be free of rank 1 over its associated order \mathfrakA_L/K, and to stricter conditions which imply that \mathfrakA_L/K is a Hopf order in the group ring K[G].

Related

• Galois scaffolds for p-extensions in characteristic p
• Galois scaffolds for cyclic pⁿ-extensions in characteristic p
• Galois scaffolds and Galois module structure in extensions of characteristic p local fields of degree p²
• Scaffolds and Generalized Integral Galois Module Structure
• Galois Scaffolds and Galois Module Structure for Totally Ramified\n C_p²-Extensions in Characteristic 0