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arXiv · 1203.5718

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

Kiran S. Kedlaya·Jonathan Pottharst·Liang Xiao
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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.

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Kiran S. Kedlaya, Jonathan Pottharst, Liang Xiao. 2013-11-19. Cohomology of arithmetic families of (phi,Gamma)-modules. https://arxiv.org/abs/1203.5718

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