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arXiv · 1406.2057

Witt-Burnside functor attached to $\mathbf{Z}_p^2$ and $p$-adic Lipschitz continuous functions

Lance Edward Miller·Benjamin Steinhurst
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Abstract

Dress and Siebeneicher gave a significant generalization of the construction of Witt vectors, by producing for any profinite group $G$, a ring-valued functor $\mathbf{W}_G$. This paper gives a concrete interpretation of the rings $\mathbf{W}_{\mathbf{Z}_p^2}(k)$ where $k$ is a field of characteristic $p > 0$ in terms of rings of Lipschitz continuous functions on the $p$-adic upper half plane $\mathbf{P}^1(\mathbf{Q}_p)$. As a consequence we show that the Krull dimensions of the rings $\mathbf{W}_{\mathbf{Z}_p^d}(k)$ are infinite for $d \geq 2$ and we show the Teichmüller representatives form an analogue of the van der Put basis for continuous functions on $\mathbf{Z}_p$.

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Lance Edward Miller, Benjamin Steinhurst. 2014-06-09. Witt-Burnside functor attached to $\mathbf{Z}_p^2$ and $p$-adic Lipschitz continuous functions. https://arxiv.org/abs/1406.2057

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