The number of non-zero coefficients of modular forms (mod p)
We give an asymptotic formula for the number of non-zero coefficients of modular forms (mod p).
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arXiv subjects
Joel Bellaiche
Publications and source records attributed to Joel Bellaiche.
Critical p-adic L-function
We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.
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Ranks of Selmer groups in an analytic family
We study the variation of the dimension of the Bloch-Kato Selmer group of a p-adic Galois representation of a number field that varies in a refined family. We show that, if one restricts ourselves to representations that are, at every place dividing $p$, crystalline, non-critically refined, and with a fixed number of non-negative Hodge-Tate weights, then the dimension of the Selmer group varies essentially lower-semi-continuously. This allows to prove lower bounds for Selmer groups "by continuity", in particular to prove some predictions of the conjecture of Bloch-Kato for modular forms.
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New examples of p-adically rigid automorphic forms
We give examples of cohomological automorphic forms for unitary groups which are $p$-adically rigid.
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The sign of Galois representations attached to automorphic forms for unitary groups
We determine the sign of the polarization of any polarized irreducible factor of a Galois representation attached to a polarized cohomological cuspidal automorphic form of Gl_n of a CM field: it is always +1, as was conjectured by Gross.
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p-adic families of Galois representations and higher rank Selmer groups
This is the final version of a book about p-adic families of Galois representations, Selmer groups, eigenvarieties and Arthur's conjectures
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Lissite de la courbe de Hecke de GL(2) aux points Eisenstein critiques
Let p be a prime number and C be the p-adic tame level 1 eigencurve introduced by Coleman-Mazur. We prove that C is smooth at the evil Eisenstein points and we give necessary and sufficient conditions for etaleness of the map to the weight space at these points in terms of p-adic zeta values. A key step is the determination at these points of the schematic reducibility locus of the pseudo-character carried by C restricted to a decomposition group at p. Then, the smoothness appears to be a consequence of the fact that the Dirichlet L-functions only have simple zeros at integers.
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Converging sequences of p-adic Galois representations and density theorems
We consider limits of p-adic Galois representations, study different notions of convergence for such representations, and prove Cebotarev-type density theorems for them.
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Sur la compatibilite entre les correspondances de Langlands locale et globale pour U(3). (On the compatibility between local and global Langlands correspondances for U(3))
Using a level-raising argument (and a result of Larsen on the image of Galois representations in compatible systems), we prove that for any automorphic representation $π$ for $\U(3)$, the $l$-adic Galois representation $ρ_l$ which is attached to $π$ by the work of Blasius and Rogawski, is the one expected by local Langlands correspondance at every finite place (at least up to semi-simplification and for a density one set of primes $l$). We rely on the work of Harris and Taylor, who have proved the same results (for $\U(n)$) assuming the base change of $π$ is square-integrable at one place. As a corollary, every automorphic representation which is tempered at an infinite number of places is tempered at every places.
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Augmentation du niveau pour U(3) (Level-Raising for U(3))
We prove, for the form of unitary group in three variables attached to a CM extension which is compact at infinity, a level-raising theorem analogous to the one of Taylor (inv. math. 98, 265-280) in the case of a quaternion algebra. We give an application to non tempered automorphic forms.
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Representations non temperees pour U(3) et conjectures de Bloch-Kato
We use $p$-adic families of automorphic forms for an unitary group in three variables, containing some non-tempered forms constructed by Rogawski, to prove some cases of the Bloch-Kato conjectures.
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