Deformations of trianguline B-pairs

TL;DR

This paper studies the deformation theory of trianguline B-pairs over any p-adic field, extending previous work for Q_p and providing new insights into the structure of deformation spaces relevant to p-adic Galois representations.

Contribution

It generalizes existing deformation results from Q_p to arbitrary p-adic fields for benign B-pairs, introducing new tangent space calculations and potential applications in number theory.

Findings

Proves tangent space dimension results for benign B-pair deformations

Extends deformation theory from Q_p to general p-adic fields

Lays groundwork for applications in Zariski density problems

Abstract

The aim of this article is to study deformation theory of trianguline B-pairs for any p-adic field. For benign B-pairs, a special good class of trianguline B-pairs, we prove a main theorem concerning tangent spaces of these deformation spaces. These are generalizations of Bellaiche-Chenevier's and Chenevier's works in the case of K=Q_p, where they used (phi,Gamma)-modules over Robba ring instead of using B-pairs. The main theorem, the author hopes, will play crucial roles in some problems of Zariski density of modular points or of crystalline points in deformation spaces of global or local p-adic Galois representations.