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arXiv · 2206.06944

Zariski density of crystalline points

Gebhard Böckle·Ashwin Iyengar·Vytautas Paškūnas
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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 $p$-adic field. We also show that these points are dense in the subspace parameterizing deformations with determinant equal to a fixed crystalline character. Our proof is purely local and works for all $p$-adic fields and all residual Galois representations.

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Gebhard Böckle, Ashwin Iyengar, Vytautas Paškūnas. 2022-06-14. Zariski density of crystalline points. https://doi.org/10.1073/pnas.2221042120

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