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# Mathematical Research Letters

## Volume 27 (2020)

### Number 1

### Ordinary $\mathrm{GL}_2 (F)$-representations in characteristic two via affine Deligne–Lusztig constructions

Pages: 141 – 187

#### Author

#### Abstract

The group $\mathrm{GL}_2$ over a local field with (residue) characteristic $2$ possesses much more smooth supercuspidal $\ell$-adic representations, than over a local field of residue characteristic $\gt 2$. One way to construct these representations is via the theory of types of Bushnell–Kutzko. We construct many of them in the cohomology of certain extended affine Deligne–Lusztig varieties attached to $\mathrm{GL}_2$ and wildly ramified maximal tori in it. Then we compare our construction with the type-theoretic one. The corresponding extended affine Deligne–Lusztig varieties were introduced in a preceding article. Also in the present case they turn out to be zero-dimensional.

This work was written during the author’s stay at the University Paris 6 (Jussieu). It was funded by a postdoctoral research grant of the Deutsche Forschungsgemeinschaft (DFG).

Received 18 March 2018

Accepted 28 November 2018