Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
Siegel varieties and -adic Siegel modular forms.
-extensions of and arithmetic cohomology modulo 2.
Solving diophantine equations
Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein.
Special values of Hilbert modular functions.
Recently, Baily has established new foundation for complex multiplication in the context of Hilbert modular functions; see [1]-[4]. However, in his treatment there is a restriction on the class of CM-points treated. Namely, the order of complex multiplications associated to the point must be the maximal order in its quotient field. The purpose of this paper is two-fold: (1) to remove the restriction just mentioned; (2) to recover a result of Tate on the conjugates of CM-points by arbitrary Galois...
Superelliptic equations arising from sums of consecutive powers
Using only elementary arguments, Cassels solved the Diophantine equation (x-1)³ + x³ + (x+1)³ = z² (with x, z ∈ ℤ). The generalization (with x, z, n ∈ ℤ and n ≥ 2) was considered by Zhongfeng Zhang who solved it for k ∈ 2,3,4 using Frey-Hellegouarch curves and their corresponding Galois representations. In this paper, by employing some sophisticated refinements of this approach, we show that the only solutions for k = 5 have x = z = 0, and that there are no solutions for k = 6. The chief innovation...
Tate conjecture for twisted Siegel modular threefolds
The l-adic representations attached to a certain noncongruence subgroup.
The level 1 weight 2 case of Serre's conjecture.
The Way to the Proof of Fermat’s Last Theorem
The weight in Serre's conjectures on modular forms.
Torsion p-adic Galois representations and a conjecture of Fontaine
Transformation Theory of Eisenstein Series.
Travaux de Wiles (et Taylor, ...), partie I
Travaux de Wiles (et Taylor, ...), partie II
Two-dimensional -adic Galois representations unramified away from
Une remarque sur les représentations locales -adiques et les congruences entre formes modulaires de Hilbert
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Wildly ramified Galois representations and a generalization of a conjecture of Serre.