On the Beilinson-Bloch-Kato conjecture for polarized motives
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908554903945216 |
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| author | Peng, Hao |
| author_facet | Peng, Hao |
| contents | We study the Beilinson-Bloch-Kato conjecture for polarized motives. In the conjugate self-dual case, we show that if the central $L$-value does not vanish, then the associated Bloch-Kato Selmer group with coefficients in a suitable local field vanishes. In the self-dual analytic rank-zero case, we reduce the conjecture to a conjecture in the endoscopic Rankin-Selberg case related to the orthogonal Gross-Prasad periods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Beilinson-Bloch-Kato conjecture for polarized motives Peng, Hao Number Theory 11F67, 11G40 We study the Beilinson-Bloch-Kato conjecture for polarized motives. In the conjugate self-dual case, we show that if the central $L$-value does not vanish, then the associated Bloch-Kato Selmer group with coefficients in a suitable local field vanishes. In the self-dual analytic rank-zero case, we reduce the conjecture to a conjecture in the endoscopic Rankin-Selberg case related to the orthogonal Gross-Prasad periods. |
| title | On the Beilinson-Bloch-Kato conjecture for polarized motives |
| topic | Number Theory 11F67, 11G40 |
| url | https://arxiv.org/abs/2509.18615 |