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

Abstract

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.

substantial revision; final refereed form, to appear in Journal of the American Mathematical Society

References in corpus (3)

• Triangulation of refined families
• Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p
• Families of trianguline representations and finite slope spaces

Cited by in corpus (7)

• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Density of potentially crystalline representations of fixed weight
• Local and global structure of connections on nonarchimedean curves
• The universal family of semi-stable p-adic Galois representations
• Frobenius modules over multivariate Robba rings
• A generalization of Kato's local epsilon-conjecture for (phi,Gamma)-modules over the Robba ring
• Relative p-adic Hodge theory, II: (phi, Gamma)-modules