This paper is the first part of a work which proves Serre's modularity conjecture. We first
prove the cases p\not=2 and odd conductor, and p= 2 and weight 2, see Theorem 1.2 …

This survey article is based on 10 lectures that we gave at the September 2019 Hausdorff
School in Bonn on" the Emerton--Gee stack and related topics", and the sections correspond …

Let $ F $ be a finite extension of $\mathbb {Q} _p $, $ p> 2$. We construct admissible unitary
completions of certain representations of $\mathrm {GL} _2 (F) $ on $ L $-vector spaces …

We explicitly construct an analytic family of n-dimensional crystalline representations by
using integral p-adic Hodge theory. This is a generalization of results by Berger, Li, and Zhu …

This survey article is based on 10 lectures that we gave at the September 2019 Hausdorff
School in Bonn on “the Emerton–Gee stack and related topics”, and the sections correspond …

A generalization of the weight part of Serre's conjecture asks for which Serre weights a given
mod p representation of the absolute Galois group of Q is modular. This set is expected to …

We prove Breuil's conjecture concerning the reduction modulo $ p $ of trianguline
representations $ V $ and of the representations $\Pi (V) $ of $\mathrm {GL} _2 (\mathbf {Q} …

Serre's modularity conjecture : a survey of the level one case | CiNii Research CiNii 国立
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