Geodesic
LOGARITHMIC DE RHAM COMPARISON FOR OPEN RIGID SPACES
Forum of Mathematics, Sigma, Tome 7 (2019)

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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 $K(\unicode[STIX]{x1D70B},1)$ (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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     author = {SHIZHANG LI and XUANYU PAN},
     title = {LOGARITHMIC {DE} {RHAM} {COMPARISON} {FOR} {OPEN} {RIGID} {SPACES}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
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     year = {2019},
     doi = {10.1017/fms.2019.27},
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SHIZHANG LI; XUANYU PAN. LOGARITHMIC DE RHAM COMPARISON FOR OPEN RIGID SPACES. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.27

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