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arXiv · 2401.03288

The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$

Guillaume Pagot
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Abstract

Let $k$ be an algebraically closed field of characteristic $2$. In this paper we describe the $(\mathbb{Z}/2\mathbb{Z})^3$-actions on $k[[z]]$ for which there is a discrete valuation ring $R$, a finite extension of the ring of Witt vectors $W(k)$, such that they can be lifted as a group of $R$-automorphisms of $R[[Z]]$. In fact the necessary and sufficient condition for such an action to lift involves only the conductor type of the corresponding extension.

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Guillaume Pagot. 2024-01-06. The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$. https://arxiv.org/abs/2401.03288

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