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arXiv · 1504.00264

Affine Deligne-Lusztig varieties of higher level and the local Langlands correspondence for $GL_2$

Alexander Ivanov
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Abstract

In the present article we define coverings of affine Deligne-Lusztig varieties attached to a connected reductive group over a local field of characteristic $p > 0$. In the case of $\GL_2$, the unramified part of the local Langlands correspondence is realized in the $\ell$-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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Alexander Ivanov. 2015-04-01. Affine Deligne-Lusztig varieties of higher level and the local Langlands correspondence for $GL_2$. https://arxiv.org/abs/1504.00264

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