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arXiv · 2603.07869

On the de Rham flip-flopping in dual towers

Gabriel Dospinescu·Wiesława Nizioł
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Abstract

We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool are comparison theorems expressing the two cohomologies as pro-\'etale cohomology of corresponding relative period sheaves that, by definition, satisfy pro-\'etale descent. As an application, we show that de Rham and Hyodo-Kato cohomologies of finite level coverings of the Drinfeld space of any dimension $d$ over $K$ are admissible as representations of $\mathbb{GL}_{d+1}(K)$.

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Gabriel Dospinescu, Wiesława Nizioł. 2026-03-09. On the de Rham flip-flopping in dual towers. https://arxiv.org/abs/2603.07869

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