Cohomology of affine Deligne-Lusztig varieties for GL2
In this paper we study affine Deligne-Lusztig varieties Xw(b) for GL2 and their étale coverings. At first, we compute them explicitly, then we determine associated representations of a certain locally-compact group, the group of rational points of the σ-stabilizer of b, in their étale cohomology....
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
18 March 2013
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| In: |
Journal of algebra
Year: 2013, Volume: 383, Pages: 42-62 |
| ISSN: | 1090-266X |
| DOI: | 10.1016/j.jalgebra.2013.03.001 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jalgebra.2013.03.001 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0021869313001099 
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| Author Notes: | A. Ivanov |
MARC
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| 520 | |a In this paper we study affine Deligne-Lusztig varieties Xw(b) for GL2 and their étale coverings. At first, we compute them explicitly, then we determine associated representations of a certain locally-compact group, the group of rational points of the σ-stabilizer of b, in their étale cohomology. Further, we study these representations by determining morphisms into the irreducible representations of the given group. In particular all cuspidal representations of level 0 of GL2 of a local field and of its inner form, which is the group of units of a quaternion algebra, occur in the cohomology. | ||
| 650 | 4 | |a Affine Deligne-Lusztig variety | |
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