English

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.

Keywords

Cite

@article{arxiv.2002.08620,
  title  = {A Composite Order Generalization of Modular Moonshine},
  author = {Satoru Urano},
  journal= {arXiv preprint arXiv:2002.08620},
  year   = {2021}
}
R2 v1 2026-06-23T13:47:49.209Z