Cohomology of arithmetic families of (phi,Gamma)-modules
Number Theory
2013-11-20 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1203.5718,
title = {Cohomology of arithmetic families of (phi,Gamma)-modules},
author = {Kiran S. Kedlaya and Jonathan Pottharst and Liang Xiao},
journal= {arXiv preprint arXiv:1203.5718},
year = {2013}
}
Comments
substantial revision; final refereed form, to appear in Journal of the American Mathematical Society