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Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms

- Frank Calegari, M. Emerton
- Mathematics
- 4 April 2007

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… Expand

Slopes of overconvergent 2-adic modular forms

- Kevin Buzzard, Frank Calegari
- MathematicsCompositio Mathematica
- 20 November 2003

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.… Expand

Modularity lifting beyond the Taylor–Wiles method

- Frank Calegari, D. Geraghty
- Mathematics
- 17 July 2012

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… Expand

Automorphic forms and rational homology 3--spheres

- Frank Calegari, N. Dunfield
- Mathematics
- 16 August 2005

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… Expand

On the ramification of Hecke algebras at Eisenstein primes

- Frank Calegari, M. Emerton
- Mathematics
- 21 November 2003

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… Expand

A counterexample to the Gouvêa–Mazur conjecture

- Kevin Buzzard, Frank Calegari
- Mathematics
- 20 November 2003

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… Expand

Nearly ordinary Galois deformations over arbitrary number fields

- Frank Calegari, B. Mazur
- MathematicsJournal of the Institute of Mathematics of…
- 17 August 2007

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… Expand

A torsion Jacquet--Langlands correspondence

- Frank Calegari, Akshay Venkatesh
- Mathematics
- 16 December 2012

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… Expand

Even Galois representations and the Fontaine–Mazur conjecture

- Frank Calegari
- Mathematics
- 20 July 2009

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… Expand

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