(\epsilon\)-isomorphisms for rank one \((\varphi,\Gamma)\)-modules over Lubin-Tate Robba rings

Inspired by Nakamura's work (arXiv:1305.0880) on \(\epsilon\)-isomorphisms for \((\varphi,\Gamma)\)-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for \(L\)-analytic Lubin-Tate \((\varphi_L,\Gamma_L)\)-modules over (relative) Robb...

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Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Malcic, Milan, Steingart, Rustam, Venjakob, Otmar, Witzelsperger, Max
Format: Article
Language:English
Subjects:
Homology
Interpolation
Isomorphism
Modules
Rings (mathematics)
Online Access:Get full text
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Summary:Inspired by Nakamura's work (arXiv:1305.0880) on \(\epsilon\)-isomorphisms for \((\varphi,\Gamma)\)-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for \(L\)-analytic Lubin-Tate \((\varphi_L,\Gamma_L)\)-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 \(\epsilon\)-isomorphisms for their Lubin-Tate deformations satisfying the desired interpolation property.
ISSN:2331-8422