We prove that the category of (rigidified) Breuil–Kisin–Fargues modules up to isogeny is Tannakian. We then introduce and classify Breuil–Kisin–Fargues modules with complex multiplication mimicking the classical theory for rational Hodge structures. In particular, we compute an avatar of a ‘$p$-adic Serre group’.

中文翻译：

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具有复数乘法的 BREUIL-KISIN-FARGUS 模块

我们证明了（刚性化的）Breuil-Kisin-Fargues 模块直到同源的范畴是 Tannakian。然后，我们引入并分类 Breuil-Kisin-Fargues 模块，其复数乘法模仿有理 Hodge 结构的经典理论。特别是，我们计算了一个 '$p$-adic Serre 组”。