Title: Cohomology of arithmetic families of (phi,Gamma)-modules Authors: Kiran S. Kedlaya, Jonathan Pottharst, Liang Xiao http://front.math.ucdavis.edu/1203.5718 Categories: math.NT Number Theory (math.AG Algebraic Geometry) Comments: fixed typos and made minor corrections; added classification of all rank one arithmetic families of (phi,Gamma)-modules, over any base Abstract: We prove the finiteness 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 classical points.
nLab page on (Phi,Gamma)-cohomology