Number Theory Seminar

We prove the existence of a new structure on the first Galois cohomology of symplectic self-dual p-adic representations of G_{Q_p} of rank two for odd primes p: a functorial decomposition into free rank one Lagrangian submodules encoding Bloch--Kato subgroups in terms of epsilon factors, mirroring an underlying symplectic structure.

This local sign decomposition has local as well as global arithmetic applications, including compatibility of the Mazur--Rubin arithmetic local constants and epsilon factors, new cases of the parity conjecture, and proof of an analogue of Rubin's conjecture on local units over ramified quadratic extensions of Q_p (joint with S. Kobayashi, K. Nakamura and K. Ota).