Zariski density of crystalline points

We show that crystalline points are Zariski dense in the deformation space of a representation of the absolute Galois group of a -adic field. We also show that these points are dense in the subspace parameterizing deformations with the determinant equal to a fixed crystalline character. Our proof is...

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Published in:Proceedings of the National Academy of Sciences - PNAS 2023-03, Vol.120 (13), p.e2221042120-e2221042120
Main Authors: Böckle, Gebhard, Iyengar, Ashwin, Paškūnas, Vytautas
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Language:English
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Deformation
Physical Sciences
Representations
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description We show that crystalline points are Zariski dense in the deformation space of a representation of the absolute Galois group of a -adic field. We also show that these points are dense in the subspace parameterizing deformations with the determinant equal to a fixed crystalline character. Our proof is purely local and works for all -adic fields and all residual Galois representations.
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subjects Deformation
Physical Sciences
Representations
title Zariski density of crystalline points
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