Abstract
In the present article we define coverings of affine Deligne–Lusztig varieties attached to a connected reductive group over a non-archimedean local field. In the case of GL2 and positive characteristic, the unramified cuspidal part of the local Langlands correspondence is realized in the ℓ-adic cohomology of these varieties. We show this by giving a detailed comparison with the realization of local Langlands via cuspidal types by Bushnell–Henniart. All proofs are purely local.
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