Eisenstein cocycles in motivic cohomology
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917840826662912 |
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| author | Sharifi, Romyar Venkatesh, Akshay |
| author_facet | Sharifi, Romyar Venkatesh, Akshay |
| contents | Several authors have studied homomorphisms from first homology groups of modular curves to the second K-group of a cyclotomic ring or a modular curve X. These maps send Manin symbols in the homology groups to Steinberg symbols of cyclotomic or Siegel units. We give a new construction of these maps and a direct proof of their Hecke equivariance, analogous to the construction of Siegel units using the universal elliptic curve. Our main tool is a 1-cocycle from GL_2(Z) to the second K-group of the function field of a suitable group scheme over X, from which the maps of interest arise by specialization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_07241 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Eisenstein cocycles in motivic cohomology Sharifi, Romyar Venkatesh, Akshay Number Theory Algebraic Geometry K-Theory and Homology 11F25, 11F75, 11G18, 14F42, 19E15, 19F15 Several authors have studied homomorphisms from first homology groups of modular curves to the second K-group of a cyclotomic ring or a modular curve X. These maps send Manin symbols in the homology groups to Steinberg symbols of cyclotomic or Siegel units. We give a new construction of these maps and a direct proof of their Hecke equivariance, analogous to the construction of Siegel units using the universal elliptic curve. Our main tool is a 1-cocycle from GL_2(Z) to the second K-group of the function field of a suitable group scheme over X, from which the maps of interest arise by specialization. |
| title | Eisenstein cocycles in motivic cohomology |
| topic | Number Theory Algebraic Geometry K-Theory and Homology 11F25, 11F75, 11G18, 14F42, 19E15, 19F15 |
| url | https://arxiv.org/abs/2011.07241 |