The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910291777814528 |
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| author | Pagot, Guillaume |
| author_facet | Pagot, Guillaume |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_03288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$ Pagot, Guillaume Algebraic Geometry Number Theory 14H30, 14H37 (Primary) 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. |
| title | The local lifting problem for $(\mathbb{Z}/2\mathbb{Z})^3$ |
| topic | Algebraic Geometry Number Theory 14H30, 14H37 (Primary) |
| url | https://arxiv.org/abs/2401.03288 |