We develop a new approach to cluster algebras, based on the notion of an upper cluster
algebra defined as an intersection of Laurent polynomial rings. Strengthening the Laurent …

Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

Abstract jats: titleAbstract</jats: title> jats: pLet jats: inline-formulajats: alternativesjats: tex-
math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …

This book (1) takes place in a now thirty years long trend of researches, initiated by Ribet
([95]) aiming at constructing “arithmetically interesting” non trivial extensions between global …

The goal of this paper is to illustrate how the techniques of locally analytic p-adic
representation theory (as developed in [28, 29, 30, 31] and [13, 14, 17]; see also [16] for a …

arXiv:2210.01404v2 [math.NT] 1 Feb 2023 Page 1 An introduction to the categorical p-adic
Langlands program Matthew Emerton, Toby Gee, and Eugen Hellmann Abstract. We give an …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …

We develop the theory of overconvergent cohomology introduced by G. Stevens, and we
use it to give a construction of eigenvarieties associated to any reductive group G over ℚ …

Critical p-adic L-functions Page 1 Invent math (2012) 189:1–60 DOI 10.1007/s00222-011-0358-z
Critical p-adic L-functions Joël Bellaïche Received: 26 August 2010 / Accepted: 15 …

Using the overconvergent cohomology modules introduced by Ash–Stevens, we construct
eigenvarieties associated with reductive groups and establish some basic geometric …