A local Sign Decomposition for Symplectic Self-dual Galois Representations

par Shinichi Kobayashi (Kyushu University & IHES)

jeudi 18 sept. 2025, 14:30 → 15:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

We present a new structure on the first Galois cohomology of families of symplectic self-dual $p$-adic representations of $G_{Q_p}$ of rank two. This is a functorial decomposition into free rank one Lagrangian submodules encoding Bloch-Kato subgroups and epsilon factors, mirroring an underlying symplectic structure. This local sign decomposition has local as well as global applications, including compatibility of the Mazur-Rubin arithmetic local constants and epsilon factors, and new cases of the parity conjecture. It also leads to a formulation and proof of an analogue of Rubin's conjecture over ramified quadratic extensions of $Q_p$, which initiates an integral Iwasawa theory for CM elliptic curves at primes of additive reduction. (Joint with A. Burungale, K. Nakamura, and K. Ota.)

 

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