• Corpus ID: 231855452

# Cohomology of $(\varphi,\Gamma)$-modules over pseudorigid spaces

@inproceedings{Bellovin2021CohomologyO,
title={Cohomology of \$(\varphi,\Gamma)\$-modules over pseudorigid spaces},
author={Rebecca Bellovin},
year={2021}
}
. We study the cohomology of families of ( ϕ, Γ)-modules with coeﬃcients in pseudoaﬃnoid algebras. We prove that they have ﬁnite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify rank-1 ( ϕ, Γ)-modules and deduce that triangulations of pseudorigid families of ( ϕ, Γ)-modules can be interpolated, extending a result of [KPX14]. We then apply this to study extended eigenvarieties at the boundary of weight space, proving in particular that the eigencurve…

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