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-adic group that splits over an unramified extension. We decompose
, the abelian category of smooth level
with coefficients in
, into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat–Tits building and Deligne–Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.
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