Congruent modular forms and anticyclotomic Iwasawa theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908608031096832 |
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| author | Nguyen, Dac-Nhan-Tam |
| author_facet | Nguyen, Dac-Nhan-Tam |
| contents | Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of Greenberg-Vatsal and Emerton-Pollack-Weston, the authors compare the cyclotomic Iwasawa $μ$ and $λ$-invariants of $f_1$ and $f_2$. We extend this to the anticyclotomic indefinite setting by comparing the BDP $p$-adic $L$-functions attached to $f_1$ and $f_2$. Using this comparison, we obtain arithmetic implications for both generalized Heegner cycles and the Iwasawa main conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruent modular forms and anticyclotomic Iwasawa theory Nguyen, Dac-Nhan-Tam Number Theory 11R23 (Primary) 11G40 (Secondary) Let $p$ be an odd prime. Consider normalized newforms $f_1,f_2$ that both satisfy the Heegner hypothesis for an imaginary quadratic field $K$ and suppose that they induce isomorphic residual Galois representations. In the work of Greenberg-Vatsal and Emerton-Pollack-Weston, the authors compare the cyclotomic Iwasawa $μ$ and $λ$-invariants of $f_1$ and $f_2$. We extend this to the anticyclotomic indefinite setting by comparing the BDP $p$-adic $L$-functions attached to $f_1$ and $f_2$. Using this comparison, we obtain arithmetic implications for both generalized Heegner cycles and the Iwasawa main conjecture. |
| title | Congruent modular forms and anticyclotomic Iwasawa theory |
| topic | Number Theory 11R23 (Primary) 11G40 (Secondary) |
| url | https://arxiv.org/abs/2503.00247 |