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arXiv · 2002.08620

A Composite Order Generalization of Modular Moonshine

Satoru Urano
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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.

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Satoru Urano. 2020-02-20. A Composite Order Generalization of Modular Moonshine. https://doi.org/10.3842/sigma.2021.110

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