We establish a $p$-adic Simpson correspondence in the spirit of Liu and Zhu for rigid analytic varieties $X$ over ${ℂ}_p$ with a liftable good reduction by constructing a new period sheaf on $X_{\mathrm{\text{ proét}}}$. To do so, we use the theory of cotangent complexes described by Beilinson and Bhatt. Then we give an integral decompletion theorem and complete the proof by local calculations. Our construction is compatible with the previous works of Faltings and Liu and Zhu.

中文翻译：

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刚性解析簇的 p 进 Simpson 对应关系

我们建立一个$p$-本着刘和朱精神的刚性分析簇的adic Simpson对应$X$超过${ℂ}_p$通过在其上建造一个新的时期梁，可提升良好的减少$X_{\mathrm{\text{ 普罗埃特}}}$。为此，我们使用 Beilinson 和 Bhatt 描述的余切复形理论。然后给出积分反完备定理并通过局部计算完成证明。我们的建筑与法尔廷斯、刘和朱之前的作品兼容。