We define a stratification of Deligne–Lusztig varieties and their parahoric analogues which we call the Drinfeld stratification. In the setting of inner forms of \({{\,\mathrm{GL}\,}}_n\), we study the cohomology of these strata and give a complete description of the unique closed stratum. We state precise conjectures on the representation-theoretic behavior of the stratification. We expect this stratification to play a central role in the investigation of geometric constructions of representations of p-adic groups.

中文翻译：

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$${{\,\mathrm{GL}\,}}_n$$ GL n 的 Drinfeld 分层

我们定义了 Deligne-Lusztig 变种及其平行类似物的分层，我们称之为 Drinfeld 分层。在\({{\,\mathrm{GL}\,}}_n\)的内在形式的设置中，我们研究了这些地层的上同调，并给出了唯一封闭地层的完整描述。我们对分层的表征理论行为提出了精确的猜想。我们期望这种分层在p- adic 群表示的几何构造的研究中发挥核心作用。