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Date | May 17, 2024 |
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Speaker | Chan-Ho Kim |

Dept. | Ewha Womans University |

Room | 27-325 |

Time | 16:00-18:00 |

We explicitly construct the rank one primitive Stark (equivalently, Kolyvagin) system extending a constant multiple of Flach’s zeta elements for semi-stable elliptic curves. As its arithmetic applications, we obtain the equivalence between a specific behavior of the Stark system and the minimal modularity lifting theorem, and we also discuss the cyclicity of the adjoint Selmer groups. Our Stark system construction yields a more refined interpretation of the collection of Flach’s zeta elements than the “geometric Euler system” approach due to Flach, Wiles, Mazur, and Weston.

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