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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.08708 |
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| _version_ | 1866917001222422528 |
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| author | Shi, Linli |
| author_facet | Shi, Linli |
| contents | We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic $L$-functions associated to cuspidal automorphic representations of $\mathrm{GU}(2,1)$, thus deducing non-triviality of the motivic classes and providing evidence for Beilinson's conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On higher regulators of Picard modular surfaces Shi, Linli Number Theory Algebraic Geometry K-Theory and Homology Representation Theory 11F67, 11F55, 11G40, 19F27 We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic $L$-functions associated to cuspidal automorphic representations of $\mathrm{GU}(2,1)$, thus deducing non-triviality of the motivic classes and providing evidence for Beilinson's conjectures. |
| title | On higher regulators of Picard modular surfaces |
| topic | Number Theory Algebraic Geometry K-Theory and Homology Representation Theory 11F67, 11F55, 11G40, 19F27 |
| url | https://arxiv.org/abs/2510.08708 |