| Résume | We explicitely construct an analytic family of n-dimensional crystalline representations by using Wach modules. This is a generalization of the result by Berger, Li and Zhu. We show that a universal deformation ring related with the above constructions is connected, by Kisin's method. This yeilds automorphy lifting theorem and potential automorphy theorem, in which the condition at $p$ is weakened. This is a joint work with S. Yasuda (RIMS, Kyoto) based on speaker's previous work. |
