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Kato's main conjecture for nonordinary modular forms

Francesc Castella, Zheng Liu, Xin Wan

math.NTarXiv:2608.29470

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 CLW.

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