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…
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…
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…
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…
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.…
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…
Irreducibility of automorphic Galois representations of GL(n), n at most 5
- Frank Calegari, Toby Gee
- Mathematics
- 26 April 2011
Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL_n(A_F), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic…
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…
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