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 \(p\)-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 i...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Gebhard Böckle, Iyengar, Ashwin, Paškūnas, Vytautas
Format: Article
Language:English
Subjects:
Crystal structure
Crystallinity
Deformation
Representations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2206.06944