Trito-non-ordinary Iwasawa theory of diagonal cycles
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918202152321024 |
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| author | Alonso, Raúl Büyükboduk, Kâzım Cauchi, Antonio Lei, Antonio |
| author_facet | Alonso, Raúl Büyükboduk, Kâzım Cauchi, Antonio Lei, Antonio |
| contents | Our goal in this paper is to introduce and study the Euler system of signed diagonal cycles associated with a trito-non-ordinary triple product of the form $f^B \times g^B \times \mathbf{h}^B$, where $f^B$ (resp. $g^B$) is a $p$-ordinary (resp. non-ordinary) eigenform on an indefinite quaternion algebra $B_{/\mathbb{Q}}$ of weight $2$, and $\mathbf{h}^B$ is a primitive Hida ($p$-ordinary) family. When $B=\mathrm{M}_2(\mathbb{Q})$ is split and $\mathbf{h}=\mathbf{h}^B$ has CM by an imaginary quadratic field, this allows us to develop the signed anticyclotomic Iwasawa theory for the base change $\mathrm{BC}_{K/\mathbb{Q}}(π_f)\times \mathrm{BC}_{K/\mathbb{Q}}(π_g)\times ψ$, where $ψ$ is a Hecke character of $K$. We formulate a signed Perrin-Riou-style Iwasawa main conjecture in this setting, and obtain a result on one inclusion in this conjecture. Our methods also allow us to extend Hsieh's construction of the balanced triple-product $p$-adic $L$-function to the trito-non-ordinary scenario, and to define its signed counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trito-non-ordinary Iwasawa theory of diagonal cycles Alonso, Raúl Büyükboduk, Kâzım Cauchi, Antonio Lei, Antonio Number Theory Our goal in this paper is to introduce and study the Euler system of signed diagonal cycles associated with a trito-non-ordinary triple product of the form $f^B \times g^B \times \mathbf{h}^B$, where $f^B$ (resp. $g^B$) is a $p$-ordinary (resp. non-ordinary) eigenform on an indefinite quaternion algebra $B_{/\mathbb{Q}}$ of weight $2$, and $\mathbf{h}^B$ is a primitive Hida ($p$-ordinary) family. When $B=\mathrm{M}_2(\mathbb{Q})$ is split and $\mathbf{h}=\mathbf{h}^B$ has CM by an imaginary quadratic field, this allows us to develop the signed anticyclotomic Iwasawa theory for the base change $\mathrm{BC}_{K/\mathbb{Q}}(π_f)\times \mathrm{BC}_{K/\mathbb{Q}}(π_g)\times ψ$, where $ψ$ is a Hecke character of $K$. We formulate a signed Perrin-Riou-style Iwasawa main conjecture in this setting, and obtain a result on one inclusion in this conjecture. Our methods also allow us to extend Hsieh's construction of the balanced triple-product $p$-adic $L$-function to the trito-non-ordinary scenario, and to define its signed counterparts. |
| title | Trito-non-ordinary Iwasawa theory of diagonal cycles |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.11511 |