Overconvergent cohomology

General Introduction

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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

arXiv:1209.0710 Universal coefficients for overconvergent cohomology and the geometry of eigenvarieties from arXiv Front: math.NT by David Hansen We prove a universal coefficients theorem for the overconvergent cohomology modules introduced by Ash and Stevens, and give several applications. In particular, we sketch a very simple construction of eigenvarieties using overconvergent cohomology and prove many instances of a conjecture of Urban on the dimensions of these spaces. For example, when the underlying reductive group is an inner form of GL(2) over a quadratic imaginary extension of the rationals, the cuspidal component of the eigenvariety is a rigid analytic curve.

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General Introduction