La conjecture de Mordell
La conjecture de Weil pour les surfaces K3.
Les courbes de Shimura
Lifting Galois representations and a conjecture of Fontaine and Mazur.
Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer
Local heights on Abelian varieties and rigid analytic uniformization.
Local Indecomposability of Hilbert Modular Galois Representations
We prove the indecomposability of the Galois representation restricted to the -decomposition group attached to a non CM nearly -ordinary weight two Hilbert modular form over a totally real field under the assumption that either the degree of over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of .