The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type
The cohomology of $p$-adic Deligne-Luszitg schemes of Coxeter type
We determine the cohomology of the closed Drinfeld stratum of $p$-Deligne--Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree, and are pairwisely non-isomorphic irreducible representations of …