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arXiv · 1909.01764

On the Iwasawa invariants of Kato's zeta elements for modular forms

Chan-Ho Kim·Jaehoon Lee·Gautier Ponsinet
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Abstract

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.

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Chan-Ho Kim, Jaehoon Lee, Gautier Ponsinet. 2019-09-04. On the Iwasawa invariants of Kato's zeta elements for modular forms. https://arxiv.org/abs/1909.01764

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