Results 1  10
of
33
Construction of some families of 2dimensional crystalline representations
, 2004
"... Abstract. We construct explicitly some analytic families of étale (ϕ, Ɣ)modules, which give rise to analytic families of 2dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and ex ..."
Abstract

Cited by 30 (4 self)
 Add to MetaCart
Abstract. We construct explicitly some analytic families of étale (ϕ, Ɣ)modules, which give rise to analytic families of 2dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular forms. Mathematics Subject Classification (2000): 11F80, 11F33, 11F85, 14F30
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 ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
(Show Context)
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.
Cohomology and Duality for (ϕ, Γ)modules over the Robba ring
 Int. Math. Research Notices
"... Given a padic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale (ϕ, Γ)module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (ϕ, Γ)modules over the R ..."
Abstract

Cited by 20 (2 self)
 Add to MetaCart
Given a padic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale (ϕ, Γ)module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (ϕ, Γ)modules over the Robba ring, of the EulerPoincaré characteristic formula and Tate local duality for padic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations. Contents 1 Preliminaries 3 1.1 padic Hodge theory and (ϕ,Γ)modules......................... 3 1.2 Slope theory of ϕmodules................................. 7 2 Cohomology of (ϕ,Γ)modules 7
Bloch and Kato’s Exponential Map: Three Explicit Formulas
 DOCUMENTA MATH.
, 2003
"... The purpose of this article is to give formulas for BlochKato’s exponential map and its dual for an absolutely crystalline padic representation V, in terms of the (ϕ,Γ)module associated to V. As a corollary of these computations, we can give a very simple and slightly improved description of Perr ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
The purpose of this article is to give formulas for BlochKato’s exponential map and its dual for an absolutely crystalline padic representation V, in terms of the (ϕ,Γ)module associated to V. As a corollary of these computations, we can give a very simple and slightly improved description of PerrinRiou’s exponential map, which interpolates BlochKato’s exponentials for the twists of V. This new description directly implies PerrinRiou’s reciprocity formula.
On period spaces for pdivisible groups
 C.R. MATH. ACAD SCI. PARIS
, 2008
"... In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine’s filtered isocrystals, and period morphisms from moduli spaces of pdivisible groups to some of these period spaces. We determine the image of these period morphisms, thereby contributing to a question of Grothend ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine’s filtered isocrystals, and period morphisms from moduli spaces of pdivisible groups to some of these period spaces. We determine the image of these period morphisms, thereby contributing to a question of Grothendieck. We give examples showing that only in rare cases the image is all of the RapoportZink period space.
Serre’s modularity conjecture (II)
, 2007
"... We provide proofs of Theorems 4.1 and 5.1 of [30]. ..."
Galois Representations and LubinTate Groups
 DOCUMENTA MATH.
, 2009
"... Using LubinTate groups, we develop a variant of Fontaine’s theory of (ϕ, Γ)modules, and we use it to give a description of the Galois stable lattices inside certain crystalline representations. ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
Using LubinTate groups, we develop a variant of Fontaine’s theory of (ϕ, Γ)modules, and we use it to give a description of the Galois stable lattices inside certain crystalline representations.
On a conjecture of Rapoport and Zink
, 2008
"... In their book Rapoport and Zink constructed rigid analytic period spaces F wa for Fontaine’s filtered isocrystals and period morphisms from moduli spaces of pdivisible groups to some of these period spaces. They conjectured the existence of an étale bijective morphism F a → F wa of rigid analytic s ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
In their book Rapoport and Zink constructed rigid analytic period spaces F wa for Fontaine’s filtered isocrystals and period morphisms from moduli spaces of pdivisible groups to some of these period spaces. They conjectured the existence of an étale bijective morphism F a → F wa of rigid analytic spaces and of interesting local systems of Qpvector spaces on F a. For those period spaces possessing period morphisms de Jong pointed out that one may take F a as the image of the period morphism, viewed as a morphism of Berkovich spaces, and take the rational Tate module of the universal pdivisible group as the desired local system on F a. In this article we construct for HodgeTate weights 0 and 1 an intrinsic Berkovich open subspace of F wa through which the period morphism factors and which we conjecture to be the image of the period morphism. We present indications supporting our conjecture and we show that only in exceptional cases our open subspace equals all of F wa.
An introduction to the theory of padic representations
 in Geometric Aspects of Dwork Theory. Vol I, II, de Gruyter
, 2004
"... by ..."
(Show Context)
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 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
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