Constructing $2$-dimensional Lubin-Tate formal groups over $\mathbb{Z}_{p}$ (I)
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912846726561792 |
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| author | Abdellatif, Ramla Sarkar, Mabud Ali |
| author_facet | Abdellatif, Ramla Sarkar, Mabud Ali |
| contents | In this paper, we construct a class of $2$-dimensional formal groups over $\mathbb{Z}_p$ that provide a higher-dimensional analogue of the usual $1$-dimensional Lubin-Tate formal groups, then we initiate the study of the extensions generated by their $p^{n}$-torsion points. For instance, we prove that the coordinates of the $p^{\infty}$-torsion points of such a formal group generate an abelian extension over a certain unramified extension of $\mathbb{Q}_{p}$, and we study some ramification properties of these abelian extensions. In particular, we prove that the extension generated by the coordinates of the $p$-torsion points is in general totally ramified. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_05637 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constructing $2$-dimensional Lubin-Tate formal groups over $\mathbb{Z}_{p}$ (I) Abdellatif, Ramla Sarkar, Mabud Ali Number Theory 11S31 In this paper, we construct a class of $2$-dimensional formal groups over $\mathbb{Z}_p$ that provide a higher-dimensional analogue of the usual $1$-dimensional Lubin-Tate formal groups, then we initiate the study of the extensions generated by their $p^{n}$-torsion points. For instance, we prove that the coordinates of the $p^{\infty}$-torsion points of such a formal group generate an abelian extension over a certain unramified extension of $\mathbb{Q}_{p}$, and we study some ramification properties of these abelian extensions. In particular, we prove that the extension generated by the coordinates of the $p$-torsion points is in general totally ramified. |
| title | Constructing $2$-dimensional Lubin-Tate formal groups over $\mathbb{Z}_{p}$ (I) |
| topic | Number Theory 11S31 |
| url | https://arxiv.org/abs/2310.05637 |