(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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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments