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  Logarithmic de Rham comparison for open rigid spaces

Li, S., & Pan, X. (2019). Logarithmic de Rham comparison for open rigid spaces. Forum of Mathematics, Sigma, 7: e32. doi:10.1017/fms.2019.27.

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Li-Pan_Logarithmic de Rham comparison for open rigid spaces_2019.pdf (Publisher version), 557KB
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Li-Pan_Logarithmic de Rham comparison for open rigid spaces_2019.pdf
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© The Author(s) 2019 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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https://doi.org/10.1017/fms.2019.27 (Publisher version)
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 Creators:
Li, Shizhang, Author
Pan, Xuanyu1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Number Theory
 Abstract: In this note, we prove the logarithmic $p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally $K(\pi,1)$ (in a certain sense) with respect to $\mathbb{F}_p$-local systems and ramified coverings along the divisor. We follow Scholze's method to produce a pro-version of the Faltings site and use this site to prove a primitive comparison theorem in our
setting. After introducing period sheaves in our setting, we prove aforesaid comparison theorem.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 53
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

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Title: Forum of Mathematics, Sigma
Source Genre: Journal
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Publ. Info: Cambridge University Press
Pages: - Volume / Issue: 7 Sequence Number: e32 Start / End Page: - Identifier: -