Cohomology of arithmetic families of (𝜑,Γ)-modules

Kedlaya, Kiran; Pottharst, Jonathan; Xiao, Liang

doi:10.1090/S0894-0347-2014-00794-3

Cohomology of arithmetic families of $(\varphi , \Gamma )$-modules
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by Kiran S. Kedlaya, Jonathan Pottharst and Liang Xiao

J. Amer. Math. Soc. 27 (2014), 1043-1115

DOI: https://doi.org/10.1090/S0894-0347-2014-00794-3

Published electronically: April 3, 2014

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Abstract:

We prove the finiteness and compatibility with base change of the $(\varphi , \Gamma )$-cohomology and the Iwasawa cohomology of arithmetic families of $(\varphi , \Gamma )$-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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