Algebraic functional equation for big Galois representations over multiple $\mathbb{Z}_p$-extensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915732591214592 |
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| author | Hao, Zeping Lim, Meng Fai |
| author_facet | Hao, Zeping Lim, Meng Fai |
| contents | We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a broad range of Iwasawa-theoretic scenarios. In particular, our result applies to the triple product of Hida families in both balanced and unbalanced cases, as well as the half-ordinary Rankin-Selberg universal deformations recently studied by the first named author and Loeffler. Our result also significantly generalizes many previously known cases of algebraic functional equations and answers a question of Greenberg. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebraic functional equation for big Galois representations over multiple $\mathbb{Z}_p$-extensions Hao, Zeping Lim, Meng Fai Number Theory We present a general approach to establish algebraic functional equations for big Galois representations over multiple $\mathbb{Z}_p$-extensions. Our result is formulated in both Selmer group and Selmer complex settings, and encompasses a broad range of Iwasawa-theoretic scenarios. In particular, our result applies to the triple product of Hida families in both balanced and unbalanced cases, as well as the half-ordinary Rankin-Selberg universal deformations recently studied by the first named author and Loeffler. Our result also significantly generalizes many previously known cases of algebraic functional equations and answers a question of Greenberg. |
| title | Algebraic functional equation for big Galois representations over multiple $\mathbb{Z}_p$-extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.10426 |