For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced from a cuspidal type. We also give a fundamental step towards the classification of cuspidal representations, identifying when certain cuspidal types induce to equivalent representations; this result is new even in the case of complex representations. Finally, we prove that the representations induced from more general types are quasi-projective, a crucial tool for extending the results here to arbitrary irreducible representations.

中文翻译：

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p-adic经典群的尖峰modul模块化表示

对于具有奇数残差特征p的非档案局部区域上的经典群，我们在特征不同于p的任意代数闭合域上构造所有的齿形表示，作为由齿形类型引起的表示。我们还朝着对皮瓣表征进行分类的基本步骤，确定何时某些皮瓣类型会诱发等效的皮囊；即使是复杂的表示形式，该结果也是新的。最后，我们证明了从更一般的类型中得出的表示是准投影的，这是将结果扩展到任意不可约表示的关键工具。