New examples of modular rigid Calabi-Yau threefolds.
The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.
No -torsion on elliptic curves over cubic number fields
We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that is not one of those.
Nombre de points des variétés de Shimura sur un corps fini
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Non-optimal levels of mod l modular representations.
Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties
In this paper we prove some non-solvable base change for Hilbert modular representations, and we use this result to show the meromorphic continuation to the entire complex plane of the zeta functions of some twisted quaternionic Shimura varieties. The zeta functions of the twisted quaternionic Shimura varieties are computed at all places.