Quantum Statistical Mechanics of the Absolute Galois Group
We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichmüller group, and the Drinfeld-Ihara i...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210712 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quantum Statistical Mechanics of the Absolute Galois Group. Yuri I. Manin and Matilde Marcolli. SIGMA 16 (2020), 038, 52 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210712 |
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Manin, Yuri I. Marcolli, Matilde 2025-12-15T15:26:58Z 2020 Quantum Statistical Mechanics of the Absolute Galois Group. Yuri I. Manin and Matilde Marcolli. SIGMA 16 (2020), 038, 52 pages 1815-0659 2020 Mathematics Subject Classification: 11G32; 11M55; 11R32; 82B10; 82C10; 58B34 arXiv:1907.13545 https://nasplib.isofts.kiev.ua/handle/123456789/210712 https://doi.org/10.3842/SIGMA.2020.038 We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichmüller group, and the Drinfeld-Ihara involution. The second-named author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593. We thank the anonymous referees for several very useful comments that significantly improve the paper, and Lieven Le Bruyn for his suggestions in a series of emails that helped us to avoid ambiguities. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Statistical Mechanics of the Absolute Galois Group Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Quantum Statistical Mechanics of the Absolute Galois Group |
| spellingShingle |
Quantum Statistical Mechanics of the Absolute Galois Group Manin, Yuri I. Marcolli, Matilde |
| title_short |
Quantum Statistical Mechanics of the Absolute Galois Group |
| title_full |
Quantum Statistical Mechanics of the Absolute Galois Group |
| title_fullStr |
Quantum Statistical Mechanics of the Absolute Galois Group |
| title_full_unstemmed |
Quantum Statistical Mechanics of the Absolute Galois Group |
| title_sort |
quantum statistical mechanics of the absolute galois group |
| author |
Manin, Yuri I. Marcolli, Matilde |
| author_facet |
Manin, Yuri I. Marcolli, Matilde |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichmüller group, and the Drinfeld-Ihara involution.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210712 |
| citation_txt |
Quantum Statistical Mechanics of the Absolute Galois Group. Yuri I. Manin and Matilde Marcolli. SIGMA 16 (2020), 038, 52 pages |
| work_keys_str_mv |
AT maninyurii quantumstatisticalmechanicsoftheabsolutegaloisgroup AT marcollimatilde quantumstatisticalmechanicsoftheabsolutegaloisgroup |
| first_indexed |
2025-12-17T12:03:41Z |
| last_indexed |
2025-12-17T12:03:41Z |
| _version_ |
1851756926628528128 |