AI 中文总结
研究\(\mathbf{Q}_p\)有限扩张上光滑恰当刚性解析空间，证明满足权重 - 单值性猜想时其平展和德拉姆上同调代数是形式的，并给出非形式的此类曲面例子。
AI 中文摘要
我们证明，若在\(\mathbf{Q}_p\)的有限扩张上的光滑恰当刚性解析空间满足权重 - 单值性猜想，其平展和德拉姆上同调代数是形式的。我们给出了上同调代数非形式的光滑恰当刚性解析曲面的例子。
英文摘要
We prove that étale and de Rham cohomology algebras of a smooth proper rigid-analytic space over a finite extension of $\mathbf{Q}_p$ are formal if the rigid-analytic space satisfies the weight-monodromy conjecture. This is achieved by showing that the underlying $E_\infty$-algebra of a monodromy-pure $E_\infty$-algebra in Weil--Deligne representations is formal. We give examples of smooth proper rigid-analytic surfaces whose cohomology algebras are not formal.
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