Cohomology of arithmetic families of (phi,Gamma)-modules
  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. 
Kiran S. Kedlaya, Jonathan Pottharst, Liang Xiao
math.NT math.AG