Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 110, 15 pages      arXiv:2002.08620      https://doi.org/10.3842/SIGMA.2021.110

A Composite Order Generalization of Modular Moonshine

Satoru Urano
Division of Mathematics, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, Ibaraki 305-8571 Japan

Received March 31, 2021, in final form December 21, 2021; Published online December 24, 2021

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.

Key words: moonshine; modular function; Brauer character; vertex operator algebra.

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References

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