  We prove the finiteness and compatibility with base change of the
(phi,Gamma)-cohomology and the Iwasawa cohomology of arithmetic families of
(phi,Gamma)-modules. Using this finiteness theorem, we show that a family of
Galois representations that is densely pointwise refined in the sense of Mazur
is actually trianguline as a family over a large subspace. In the case of the
Coleman-Mazur eigencurve, we determine the behavior at all points.
