投稿

研讨会: 自守形式的岩泽理论, 韩国高等研究院 (KIAS), 2022

Name: %E7%A0%94%E8%AE%A8%E4%BC%9A:%20%E8%87%AA%E5%AE%88%E5%BD%A2%E5%BC%8F%E7%9A%84%E5%B2%A9%E6%B3%BD%E7%90%86%E8%AE%BA,%20%E9%9F%A9%E5%9B%BD%E9%AB%98%E7%AD%89%E7%A0%94%E7%A9%B6%E9%99%A2%20(KIAS),%202022
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2022-12-28 20:00:29

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http://events.kias.re.kr/h/IWIA/?pageNo=4827 最近, 椭圆曲线与模形式的岩泽理论有了重大进展. 值得注意的是, 这些进展对千禧年大奖难题之一的 BSD 猜想有着重要的应用. 本次研讨会的主要目标是介绍 Castella, 刘峥和万昕最近关于 GU(3,1) 上自守形式的 Iwasawa 主猜想的工作中的诸多细节 (arXiv:2109.08375). 特别地, 这项工作对证明一大类具有超奇异约化的椭圆曲线的 Iwasawa 主猜想起到了重要作用. 1. Wan 1: Automorphic forms, Eisenstein series, and Greenberg's main conjecture We discuss Hermitian modular forms, Eisenstein series on unitary groups, and Greenberg's main conjecture. 2. Castella 1: Kobayashi's main conjecture We discuss the relation between Greenberg's main conjecture and Kobayashi's main conjecture. 3. Castella 2: Cuspidal Hida theory We discuss cuspidal Hida theory for GU(3,1). 4. Liu 1: Non-cuspidal Hida theory We discuss non-cuspidal Hida theory for GU(3,1). 5. Wan 2: General strategy We discuss the general strategy of the proof of the main conjecture. 6. Liu 2: The constant term We discuss the computation of the constant term of Eisenstein series. 7. Castella 3: Kobayashi's main conjecture 2 We continue the discussion on the relation between Greenberg's main conjecture and Kobayashi's main conjecture. 8. Liu 3: Fourier-Jacobi coefficients We discuss the computation of non-degenerate Fourier-Jacobi coefficients. 9. Wan 3: Lattice construction and the conclusion We discuss the lattice construction and conclude the proof of the main conjecture. appeared in: Forum of Mathematics, Sigma, 10, E110. doi:10.1017/fms.2022.95

数学