%0 Journal Article %T An upper bound on the exceptional characteristics for Lusztig's character formula %A Peter Fiebig %J Mathematics %D 2008 %I arXiv %X We develop and study a Lefschetz theory in a combinatorial category associated to a root system and derive an upper bound on the exceptional characteristics for Lusztig's formula for the simple rational characters of a reductive algebraic group. Our bound is huge compared to the Coxeter number. It is, however, given by an explicit formula. %U http://arxiv.org/abs/0811.1674v2