On the indivisibility of derived Kato’s Euler systems and the main conjecture for modular forms

Chan-Ho Kim ^[1] ; Myoungil Kim ^[2] ; Hae-Sang Sun ^[2]
1. [1] Korea Institute for Advanced Study
  
  Korea Institute for Advanced Study
  
  Corea del Sur
2. [2] Ulsan National Institute of Science and Technology
  
  Ulsan National Institute of Science and Technology
  
  Corea del Sur
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
Idioma: inglés
DOI: 10.1007/s00029-020-00554-w
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Resumen
- We provide a simple and efficient numerical criterion to verify the Iwasawa main conjecture and the indivisibility of derived Kato’s Euler systems for modular forms of weight two at any good prime under mild assumptions. In the ordinary case, the criterion works for all members of a Hida family once and for all. The key ingredient is the explicit computation of the integral image of the derived Kato’s Euler systems under the dual exponential map. We provide explicit new examples at the end. This work does not appeal to the Eisenstein congruence method at all.