A universal Euler system for GSp(4)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914508257099776 |
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| author | Loeffler, David Zerbes, Sarah Livia |
| author_facet | Loeffler, David Zerbes, Sarah Livia |
| contents | In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms for GSp(4). This construction depended on various arbitrary choices of local test data. In this paper, we use multiplicity-one results for smooth representations to determine how these Euler system classes depend on the choice of test data, showing that all of these classes lie in a 1-dimensional space and are explicit multiples (given by local zeta-integrals) of a "universal" class independent of the choice of test data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_12576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A universal Euler system for GSp(4) Loeffler, David Zerbes, Sarah Livia Number Theory 11F46, 11F67, 11F80 In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms for GSp(4). This construction depended on various arbitrary choices of local test data. In this paper, we use multiplicity-one results for smooth representations to determine how these Euler system classes depend on the choice of test data, showing that all of these classes lie in a 1-dimensional space and are explicit multiples (given by local zeta-integrals) of a "universal" class independent of the choice of test data. |
| title | A universal Euler system for GSp(4) |
| topic | Number Theory 11F46, 11F67, 11F80 |
| url | https://arxiv.org/abs/2411.12576 |