Congruence modules related to Eisenstein series
Congruence Properties and Density Problems for the Fourier Coefficients of Modular Forms.
Congruence properties of the hyperkloosterman sum
Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture
Let be a positive integer divisible by 4, a prime, an elliptic cuspidal eigenform (ordinary at ) of weight , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives and , where is the motif attached to . More precisely, we prove that under certain conditions the -adic valuation of the algebraic part of the symmetric square -function of evaluated at provides a lower bound for the -adic valuation of the order of the Pontryagin...
Congruences between cusp forms and the geometry of Jacobians of modular curves.
Congruences between modular forms and lowering the level mod
In this article we study the behavior of inertia groups for modular Galois mod representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).
Congruences between Siegel modular forms on the level of group cohomology
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...
Congruences for Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two.
Congruences for Eigenvalues of Hecke Operators on SL2(Z).
Congruences for Siegel modular forms
We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree . In particular, we determine when an analog of Atkin’s -operator applied to a Siegel modular form of degree is nonzero modulo a prime . Furthermore, we discuss explicit examples to illustrate our results.
Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups.
Control theorems of -nearly ordinary cohomology groups for
Cuspidal groups, ordinary Eisenstein series, and Kubota-Leopoldt p-adic L-functions
Equivariant K-theory and representations of Hecke algebras. II.
Euler system for Galois deformations
In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation and the...
Euler systems obtained from congruences between Hilbert modular forms
Exceptional congruences for powers of the partition function
Fields of definition of -curves
Let be a -curve with no complex multiplication. In this note we characterize the number fields such that there is a curve isogenous to having all the isogenies between its Galois conjugates defined over , and also the curves isogenous to defined over a number field such that the abelian variety Res obtained by restriction of scalars is a product of abelian varieties of GL-type.
Formes automorphes cuspidales pour sur un corps quadratique imaginaire. Valeurs spéciales de fonctions et congruences
Formes compagnons et complexe BGG dual pour
On montre, sous certaines hypothèses un résultat en direction de la conjecture de Serre pour formulée dans un autre article avec F. Herzig : si la représentation résiduelle associée à une forme de Siegel de genre , de niveau premier à , -ordinaire de poids -petit, laisse stables deux droites (au lieu d’une) dans un plan lagrangien, alors cette forme possède une forme compagnon de poids prescrit. Notre méthode consiste à traduire, grâce au théorème de comparaison mod. de Faltings, l’existence...