Cohomology of arithmetic families of (phi,Gamma)-modules

Details Cohomology of arithmetic families of (phi,Gamma)-modules Cohomology of arithmetic families of (phi,Gamma)-modules

2012-03-26

arxiv.org/abs/1203.5718v1

Mathematics

Number Theory

Scientific paper

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.

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