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Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms
Let Goo be a semisimple real Lie group with unitary dual Goo- We produce new upper bounds for the multiplicities with which representations ^ e of cohomological type appear in certain spaces of cusp
Slopes of overconvergent 2-adic modular forms
We explicitly compute all the slopes of the Hecke operator U2 acting on overconvergent 2-adic level 1 cusp forms of weight 0: the nth slope is 1 + 2v((3n)!/n!), where v denotes the 2-adic valuation.
Modularity lifting beyond the Taylor–Wiles method
We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been
Automorphic forms and rational homology 3--spheres
We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with
On the ramification of Hecke algebras at Eisenstein primes
Fix a prime p, and a modular residual representation ρ : GQ → GL2(Fp). Suppose f is a normalized cuspidal Hecke eigenform of some level N and weight k that gives rise to ρ, and let Kf denote the
A counterexample to the Gouvêa–Mazur conjecture
Abstract Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this Note, we exhibit examples
Nearly ordinary Galois deformations over arbitrary number fields
Abstract Let K be an arbitrary number field, and let ρ : Gal($\math{\bar{K}}$/K) → GL2(E) be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary
A torsion Jacquet--Langlands correspondence
We study torsion in the homology of arithmetic groups and give evidence that it plays a role in the Langlands program. We prove, among other results, a numerical form of a Jacquet--Langlands
Even Galois representations and the Fontaine–Mazur conjecture
We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of $\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})$ with distinct Hodge–Tate