Recently, with A. Burungale, K. Nakamura and K. Ota, we established a fundamental decomposition of Galois cohomology for families (e.g. universal deformation) of symplectic self-dual p-adic representations of G_{Q_p} of rank 2.
This decomposition gives a relation between local Bloch-Kato subgroups and local root numbers in the family.
There are a number of applications like a new case of the p-parity conjecture, Mazur-Rubin arithmetic local constant, CM Iwasawa theory at ramified primes.
In this talk I would like to elaborate on the significance of this decomposition.