$ε$-isomorphisms for rank one $(φ,Γ)$-modules over Lubin-Tate Robba rings
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915242205773824 |
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| author | Malcic, Milan Steingart, Rustam Venjakob, Otmar Witzelsperger, Max |
| author_facet | Malcic, Milan Steingart, Rustam Venjakob, Otmar Witzelsperger, Max |
| contents | Inspired by Nakamura's work (arXiv:1305.0880) on $ε$-isomorphisms for $(φ,Γ)$-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for $L$-analytic Lubin-Tate $(φ_L,Γ_L)$-modules over (relative) Robba rings for any finite extension $L$ of $\mathbb{Q}_p.$ In contrast to Kato's and Nakamura's setting, our conjecture involves $L$-analytic cohomology instead of continuous cohomology within the generalized Herr complex. Similarly, we restrict to the identity components of $D_{cris}$ and $D_{dR},$ respectively. For rank one modules of the above type or slightly more generally for trianguline ones, we construct $ε$-isomorphisms for their Lubin-Tate deformations satisfying the desired interpolation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ε$-isomorphisms for rank one $(φ,Γ)$-modules over Lubin-Tate Robba rings Malcic, Milan Steingart, Rustam Venjakob, Otmar Witzelsperger, Max Number Theory 11F80 Inspired by Nakamura's work (arXiv:1305.0880) on $ε$-isomorphisms for $(φ,Γ)$-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for $L$-analytic Lubin-Tate $(φ_L,Γ_L)$-modules over (relative) Robba rings for any finite extension $L$ of $\mathbb{Q}_p.$ In contrast to Kato's and Nakamura's setting, our conjecture involves $L$-analytic cohomology instead of continuous cohomology within the generalized Herr complex. Similarly, we restrict to the identity components of $D_{cris}$ and $D_{dR},$ respectively. For rank one modules of the above type or slightly more generally for trianguline ones, we construct $ε$-isomorphisms for their Lubin-Tate deformations satisfying the desired interpolation property. |
| title | $ε$-isomorphisms for rank one $(φ,Γ)$-modules over Lubin-Tate Robba rings |
| topic | Number Theory 11F80 |
| url | https://arxiv.org/abs/2404.09974 |