Galois scaffolds for $p$-extensions in characteristic $p$

G. Griffith Elder; Kevin Keating

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arXiv · 2308.02775

Galois scaffolds for $p$-extensions in characteristic $p$

G. Griffith Elder·Kevin Keating

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Abstract

Let $K$ be a local field of characteristic $p>0$ with perfect residue field and let $G$ be a finite $p$-group. In this paper we use Saltman's construction of a generic $G$-extension of rings of characteristic $p$ to construct totally ramified $G$-extensions $L/K$ that have Galois scaffolds. We specialize this construction to produce $G$-extensions $L/K$ such that the ring of integers $O_L$ is free of rank 1 over its associated order $A_0$, and extensions such that $A_0$ is a Hopf order in the group ring $K[G]$.

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G. Griffith Elder, Kevin Keating. 2023-08-05. Galois scaffolds for $p$-extensions in characteristic $p$. https://arxiv.org/abs/2308.02775

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