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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Bibliographic Details
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
Format: Article
Language:English
Subjects:
Deformation
Physical Sciences
Representations
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Summary: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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.2221042120