Introduces crystalline (ϕ,Γ)-modules over Ã_K⁺ and shows their category is equivalent to crystalline ℤ_p-representations of Gal(K), generalizing Berger's unramified case.
A remark on an integral structure of the imperfect coefficient ring of $(\varphi,\Gamma)$-modules
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abstract
Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(\varphi,\Gamma)$-modules defined by Jean-Marc Fontaine. We prove that the canonical map $W(k_{K_\infty})[[\mu]]\rightarrow \mathbb{A}_K\cap A_\mathrm{inf}$ is an isomorphism, even if $K$ is ramified. This fact was remarked by Nathalie Wach without proof.
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math.NT 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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On the $(\varphi,\Gamma)$-modules corresponding to crystalline representations
Introduces crystalline (ϕ,Γ)-modules over Ã_K⁺ and shows their category is equivalent to crystalline ℤ_p-representations of Gal(K), generalizing Berger's unramified case.