Deligne-Lusztig varieties and period domains over finite fields

Details Deligne-Lusztig varieties and period domains over finite fields Deligne-Lusztig varieties and period domains over finite fields

2007-05-11

arxiv.org/abs/0705.1646v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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