Math Seminars.
Sasha Orlik (University of Cologne),
The cohomology of period domains over finite fields.
Period domains are open subsets of generalized flag varieties, which are
described by semistable conditions. In the case of a local ground field
these period domains are open admissible subsets in the sense of rigid
algebraic geometry, whereas in the finite ground field case one gets open
subvarieties. The goal of the talk is to present the strategy of the
compution of the l-adic cohomology of period domains. The result confirms
a conjecture of Kottwitz and Rapoport.