(Phi,Gamma)cohomology

General Introduction
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Search results
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Online References
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Title: Cohomology of arithmetic families of (phi,Gamma)modules Authors: Kiran S. Kedlaya, Jonathan Pottharst, Liang Xiao http://front.math.ucdavis.edu/1203.5718 Categories: math.NT Number Theory (math.AG Algebraic Geometry) Comments: fixed typos and made minor corrections; added classification of all rank one arithmetic families of (phi,Gamma)modules, over any base Abstract: 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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Other Information
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