A Composite Order Generalization of Modular Moonshine
Representation Theory
2021-12-28 v3 Group Theory
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 vanishing of Tate cohomology for Fricke elements of the Monster.
Cite
@article{arxiv.2002.08620,
title = {A Composite Order Generalization of Modular Moonshine},
author = {Satoru Urano},
journal= {arXiv preprint arXiv:2002.08620},
year = {2021}
}