On the Cohomology of Deligne-Lusztig Varieties

Mathematics – Representation Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

41 pages

Scientific paper

In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. These degrees are a necessary piece of data in the geometric version of Brou\'e's abelian defect group conjecture, and can be used to verify this geometric conjecture in new cases. The geometric version of Brou\'e's conjecture should produce a more combinatorially defined derived equivalence, called a perverse equivalence. We prove that our conjectural degree is an integer (which is not obvious) and has the correct parity for a perfect isometry, and verify that it induces a perverse equivalence for all unipotent blocks of groups of Lie type with cyclic defect groups, whenever the shape of the Brauer tree is known (i.e., not E7 and E8). It has also been used to find perverse equivalences for some non-cyclic cases. This paper is a contribution to the conjectural description of the exact form of a derived equivalence proving Brou\'e's conjecture for groups of Lie type.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On the Cohomology of Deligne-Lusztig Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Cohomology of Deligne-Lusztig Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Cohomology of Deligne-Lusztig Varieties will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-33734

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.