Deligne-Lusztig varieties and period domains over finite fields

Abstract

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.

16 pages, reference added to the paper of X. He (arXiv:0707.0259) in which the affineness conjecture for DL-varieties is proved

Cited by in corpus (2)

• Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties
• The fundamental group of period domains over finite fields