A Composite Order Generalization of Modular Moonshine
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211417 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Composite Order Generalization of Modular Moonshine. Satoru Urano. SIGMA 17 (2021), 110, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862680757019869184 |
|---|---|
| author | Urano, Satoru |
| author_facet | Urano, Satoru |
| citation_txt | A Composite Order Generalization of Modular Moonshine. Satoru Urano. SIGMA 17 (2021), 110, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-16T23:54:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211417 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T23:54:25Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Urano, Satoru 2026-01-02T08:28:27Z 2021 A Composite Order Generalization of Modular Moonshine. Satoru Urano. SIGMA 17 (2021), 110, 15 pages 1815-0659 2020 Mathematics Subject Classification: 11F22; 11F85; 17B69; 20C11; 20C20 arXiv:2002.08620 https://nasplib.isofts.kiev.ua/handle/123456789/211417 https://doi.org/10.3842/SIGMA.2021.110 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. I would like to thank Scott Carnahan for many helpful comments and advice. I would also like to thank the anonymous referees for many helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Composite Order Generalization of Modular Moonshine Article published earlier |
| spellingShingle | A Composite Order Generalization of Modular Moonshine Urano, Satoru |
| title | A Composite Order Generalization of Modular Moonshine |
| title_full | A Composite Order Generalization of Modular Moonshine |
| title_fullStr | A Composite Order Generalization of Modular Moonshine |
| title_full_unstemmed | A Composite Order Generalization of Modular Moonshine |
| title_short | A Composite Order Generalization of Modular Moonshine |
| title_sort | composite order generalization of modular moonshine |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211417 |
| work_keys_str_mv | AT uranosatoru acompositeordergeneralizationofmodularmoonshine AT uranosatoru compositeordergeneralizationofmodularmoonshine |