First explicit reciprocity law for unitary Friedberg--Jacquet periods
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912894518558720 |
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| author | Corato-Zanarella, Murilo |
| author_facet | Corato-Zanarella, Murilo |
| contents | Consider a unitary group $G(\mathbb{A}_{F^+})=U_{2r}(\mathbb{A}_{F^+})$ over a CM extension $F/F^+$ with $G(\mathbb{A}_\infty)$ compact. In this article, we study the Beilinson--Bloch--Kato conjecture for motives associated to irreducible cuspidal automorphic representations $π$ of $G(\mathbb{A}_{F^+}).$ We prove that if $π$ is distinguished by the unitary Friedberg--Jacquet period, then the Bloch--Kato Selmer group (with coefficients in a favorable field) of the motive of $Π=\mathrm{BC}(π)$ vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09831 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | First explicit reciprocity law for unitary Friedberg--Jacquet periods Corato-Zanarella, Murilo Number Theory Consider a unitary group $G(\mathbb{A}_{F^+})=U_{2r}(\mathbb{A}_{F^+})$ over a CM extension $F/F^+$ with $G(\mathbb{A}_\infty)$ compact. In this article, we study the Beilinson--Bloch--Kato conjecture for motives associated to irreducible cuspidal automorphic representations $π$ of $G(\mathbb{A}_{F^+}).$ We prove that if $π$ is distinguished by the unitary Friedberg--Jacquet period, then the Bloch--Kato Selmer group (with coefficients in a favorable field) of the motive of $Π=\mathrm{BC}(π)$ vanishes. |
| title | First explicit reciprocity law for unitary Friedberg--Jacquet periods |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.09831 |