Unipotent elements in small characteristic
- Cite this article as:
- Lusztig, G. Transformation Groups (2005) 10: 449. doi:10.1007/s00031-005-0405-1
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Let G be a reductive connected algebraic group over an algebraically closed field of characteristic exponent p ≥ 1. One of the aims of this paper is to present a picture of the unipotent elements of G which should apply for arbitrary p and is as close as possible to the picture for p = 1. Another aim is the study of Bu, the variety of Borel subgroups of G containing a unipotent element u. It is known [Sp] that when p is a good prime, the l-adic cohomology spaces of Bu are pure. We would like to prove a similar result in the case where p is a bad prime. We present a method by which this can be achieved in a number of cases.