We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p -adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space.

中文翻译：

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刚性簇和霍奇对称上的线丛

我们证明了非阿基米德域上适当光滑刚性解析簇的低阶霍奇数的几个相关结果。我们的论点依赖于相关 Picard 变体的已知结构定理，以及 p-adic Hodge 理论的最新进展。我们还定义了一个与任何光滑的适当刚性空间自然相关的刚性解析 Albanese。