On the Iwasawa invariants of Kato's zeta elements for modular forms
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866918446435926016 |
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| author | Kim, Chan-Ho Lee, Jaehoon Ponsinet, Gautier |
| author_facet | Kim, Chan-Ho Lee, Jaehoon Ponsinet, Gautier |
| contents | We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato's main conjecture without $p$-adic $L$-functions under congruences. It generalizes the work of Greenberg-Vatsal, Emerton-Pollack-Weston, B.D. Kim, Greenberg-Iovita-Pollack, and one of us simultaneously. As a consequence, we establish the propagation of Kato's main conjecture for modular forms of higher weight at arbitrary good prime under the assumption on the mod $p$ non-vanishing of Kato's zeta elements. The application to the $\pm$ and $\sharp/\flat$-Iwasawa theory for modular forms is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_01764 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the Iwasawa invariants of Kato's zeta elements for modular forms Kim, Chan-Ho Lee, Jaehoon Ponsinet, Gautier Number Theory We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato's main conjecture without $p$-adic $L$-functions under congruences. It generalizes the work of Greenberg-Vatsal, Emerton-Pollack-Weston, B.D. Kim, Greenberg-Iovita-Pollack, and one of us simultaneously. As a consequence, we establish the propagation of Kato's main conjecture for modular forms of higher weight at arbitrary good prime under the assumption on the mod $p$ non-vanishing of Kato's zeta elements. The application to the $\pm$ and $\sharp/\flat$-Iwasawa theory for modular forms is also discussed. |
| title | On the Iwasawa invariants of Kato's zeta elements for modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/1909.01764 |