Zariski density of crystalline points.

Böckle, Gebhard; Iyengar, Ashwin; Paškūnas, Vytautas · Proc Natl Acad Sci U S A · 2023

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Abstract

We show that crystalline points are Zariski dense in the deformation space of a representation of the absolute Galois group of a <i>p</i>-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 <i>p</i>-adic fields and all residual Galois representations.