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Deligne-Lusztig varieties and period domains over finite fields

S. Orlik, M. Rapoport

Number 27
Author Michael Rapoport
Year 2007

We prove that the Drinfeld halfspace is essentially the only Deligne-Lusztig variety which is at the same time a period domain over a finite field. This is done by comparing a cohomology vanishing theorem for DL-varieties, due to Digne, Michel, and Rouquier, with a non-vanishing theorem for PD, due to the first author. We also discuss an affineness criterion for DL-varieties.

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