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Resolutions for representations of reductive \(p\)-adic groups via their buildings. (English) Zbl 1210.22012

Let \({\mathcal G}_{\mathbb K}\) be a reductive \(p\)-adic group over a non-archimedean local field \({\mathbb K}\). The authors use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the affine Bruhat-Tits building and to establish that these are acyclic and compute homology and cohomology with these coefficients. This implies Bernstein’s result that certain subcategories of the category of representations are Serre subcategories. They also get results for convex subcomplexes of the building. Following work of Korman, this leads to trace formulas for admissible representations.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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References:

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