Wednesday, November 2, 2011 - 16:00
1 hour (actually 50 minutes)
This is joint work with Mitya Boyarchenko. We construct a special hypersurface X over a finite field, which has the property of "maximality", meaning that it has the maximum number of rational points relative to its topology. Our variety is derived from a certain unipotent algebraic group, in an analogous manner as Deligne-Lusztig varieties are derived from reductive algebraic groups. As a consequence, the cohomology of X can be shown to realize a piece of the local Langlands correspondence for certain wild Weil parameters of low conductor.