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PreprintCC BY 4.0arXiv

Kato's main conjecture for nonordinary modular forms

  • Francesc Castella
  • Zheng Liu
  • Xin Wan
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Abstract

We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the conjecture in terms of signed Selmer groups due to Lei-Loeffler-Zerbes, certain p-adic families of Rankin-Eisenstein classes arising from the work of Lei-Loeffler-Zerbes and Kings-Loeffler-Zerbes, and the lower bound divisibility in an Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions obtained in our earlier work \cite{CLW}.

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Cite

BibTeXRIS
BibTeX
@misc{castella2026katos,
  title = {{Kato's main conjecture for nonordinary modular forms}},
  author = {Francesc Castella and Zheng Liu and Xin Wan},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29470},
  eprint = {2608.29470},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29470},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Kato's main conjecture for nonordinary modular forms
AU  - Francesc Castella
AU  - Zheng Liu
AU  - Xin Wan
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29470
UR  - https://arxiv.org/abs/2608.29470
AB  - We prove Kato's main conjecture for modular forms at nonordinary primes for weights in the Fontaine-Laffaille range. The key ingredients in the proof are a reformulation of the conjecture in terms of signed Selmer groups due to Lei-Loeffler-Zerbes, certain p-adic families of Rankin-Eisenstein classes arising from the work of Lei-Loeffler-Zerbes and Kings-Loeffler-Zerbes, and the lower bound divisibility in an Iwasawa-Greenberg main conjecture for Rankin-Selberg p-adic L-functions obtained in our earlier work \cite{CLW}.
ER  -