A local sign decomposition for symplectic self-dual Galois representations I & II
报告专家：Professor Kobayashi and Professor Nakamura (Kyushu University)
报告时间：2025年3月10日（星期一）下午 14:30-15:30，15:45-16:45
报告地点：国家天元数学西南中心516
报告摘要：For symplectic self-dual Galois representations, the Bloch-Kato conjecture suggests the associated epsilon factors to be pivotal to their arithmetic. e.g. The parity conjecture. We present a functorial decomposition of Galois cohomology of such p-adic family of representations of $G_{Q_p}$ of rank two, mirroring an underlying symplectic structure.
In the first talk, we explain the meaning and applications of our theorem, especially, Iwasawa theory of CM elliptic curves at ramified primes, similar to the inert case developed by K. Rubin and our previous work.
In the second talk, we explain the outline of the proof of our main theorem and its relations to Kato's epsilon conjecture and the p-adic Langlands correspondence.
This is a joint work with A. Burungale and K. Ota.
专家简介：
Shinichi Kobayashi (小林 真一)教授任职于日本九州大学，主要研究方向为p-进算术理论和Iwasawa理论，多项研究成果发表于Annals of Mathematics，Inventiones mathematicae等期刊。
Kentaro Nakamura (中村 健太郎)教授任职于日本九州大学，主要研究方向为p-进朗兰兹对应和Iwasawa理论，研究工作发表于Inventiones mathematicae等期刊。
邀请人：许宾
