A Composite Order Generalization of Modular Moonshine

Abstract

We introduce a generalization of Brauer character to allow arbitrary finite-length modules over discrete valuation rings. We show that the generalized super Brauer character of Tate cohomology is a linear combination of trace functions. Using this result, we find a counterexample to a conjecture of Borcherds about the vanishing of Tate cohomology for Fricke elements of the Monster.