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The FontaineMazur conjecture for GL2
 Journal of the A.M.S
"... 1. BreuilMézard conjecture and the padic local Langlands 644 (1.1) The BreuilMézard conjecture 644 (1.2) Review of Colmez’s functor 647 ..."
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1. BreuilMézard conjecture and the padic local Langlands 644 (1.1) The BreuilMézard conjecture 644 (1.2) Review of Colmez’s functor 647
On Serre’s conjecture for 2dimensional mod p representations of Gal(Q̄/Q)
"... We prove the existence in many cases of minimally ramified padic lifts of 2dimensional continuous, odd, absolutely irreducible, mod p representations ¯ρ of the absolute Galois group of Q. It is predicted by Serre’s conjecture that such representations arise from newforms of optimal level and weig ..."
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We prove the existence in many cases of minimally ramified padic lifts of 2dimensional continuous, odd, absolutely irreducible, mod p representations ¯ρ of the absolute Galois group of Q. It is predicted by Serre’s conjecture that such representations arise from newforms of optimal level and weight. Using these minimal lifts, and arguments using compatible systems, we prove some cases of Serre’s conjectures in low levels and weights. For instance we prove that there are no irreducible (p, p) type group schemes over Z. We prove that a ¯ρ as above of Artin conductor 1 and Serre weight 12 arises from the Ramanujan Deltafunction. In the last part of the paper we present arguments that reduce Serre’s conjecture to proving generalisations of modularity lifting theorems of the type pioneered by Wiles.
A localglobal compatibility conjecture in the padic Langlands programme for GL2/Q
 Special Issue: In honor of John Coates, Part 2 of
"... 3. The local padic Langlands conjecture for GL2/Qp 14 ..."
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3. The local padic Langlands conjecture for GL2/Qp 14
ON SERRE’S MODULARITY CONJECTURE FOR 2DIMENSIONAL MOD p REPRESENTATIONS OF ... Unramified Outside p
, 2005
"... We prove the level one case of Serre’s conjecture. Namely, we prove that any continuous, odd, irreducible representation ¯ρ: Gal ( ¯ Q/Q) → GL2(Fp) which is unramified outside p arises from a cuspidal eigenform in S k(¯ρ)(SL2(Z)). The proof relies on the methods introduced in an earlier joint wor ..."
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We prove the level one case of Serre’s conjecture. Namely, we prove that any continuous, odd, irreducible representation ¯ρ: Gal ( ¯ Q/Q) → GL2(Fp) which is unramified outside p arises from a cuspidal eigenform in S k(¯ρ)(SL2(Z)). The proof relies on the methods introduced in an earlier joint work with JP. Wintenberger, together with a new method of “weight reduction”.
Serre’s modularity conjecture (II)
, 2007
"... We provide proofs of Theorems 4.1 and 5.1 of [30]. ..."
Euler systems for RankinSelberg convolutions of modular forms
 Annals of Math
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An introduction to the theory of padic representations
 in Geometric Aspects of Dwork Theory. Vol I, II, de Gruyter
, 2004
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Iwasawa theory for modular forms at supersingular primes
 Compositio Math
"... where explicit reference to the results of others is made. Parts of this work (Chapter 7) were performed in collaboration with Sarah Zerbes in Michaelmas term 2009 and Lent term 2010, with the exception of Proposition 7.4.5, which was joint work with David Loeffler. The proofs in this chapter are ei ..."
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where explicit reference to the results of others is made. Parts of this work (Chapter 7) were performed in collaboration with Sarah Zerbes in Michaelmas term 2009 and Lent term 2010, with the exception of Proposition 7.4.5, which was joint work with David Loeffler. The proofs in this chapter are either entirely mine or those to which I have contributed. Most of the work contained in this thesis has been submitted for publication and preprints are available on the arXiv website:
On reductions of families of crystalline Galois representations
 Doc. Math
"... Let K be any finite unramified extension of Qp. We construct analytic families of étale (ϕ,ΓK)modules which correspond to all the effective crystalline characters and some families of ndimensional crystalline Galois representations of GK =Gal ( ¯ Qp/K). As an application, we compute semisimplifie ..."
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Cited by 5 (1 self)
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Let K be any finite unramified extension of Qp. We construct analytic families of étale (ϕ,ΓK)modules which correspond to all the effective crystalline characters and some families of ndimensional crystalline Galois representations of GK =Gal ( ¯ Qp/K). As an application, we compute semisimplified modulo p reductions for some of these families. Contents
Zerbes: Wach Modules and Iwasawa Theory for Modular Forms
 Asian Journal of Mathematics
, 2010
"... This paper is made available online in accordance with publisher policies. Please scroll down to view the document itself. Please refer to the repository record for this item and our policy information available from the repository home page for further information. To see the final version of this ..."
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Cited by 5 (2 self)
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This paper is made available online in accordance with publisher policies. Please scroll down to view the document itself. Please refer to the repository record for this item and our policy information available from the repository home page for further information. To see the final version of this paper please visit the publisher’s website. Access to the published version may require a subscription.