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For Hida theory on $GU(2,2)$ can $p$ be inert in the imaginary quadratic field $K$?

I am familiar with the theory of Hida families of modular forms, so Hida theory on $GL_2$, but I am not familiar with Hida theory on any other algebraic groups. My question concerns Hida families of ...
Will Dukeminier's user avatar