Iwasawa theory for modular forms and Wach modules

Let f be a modular form and p a supersingular for f. The Iwasawa theory for f over the Zp-cyclotomic extension is more difficult than the ordinary case for two reasons: 1. The classical p-adic L-functions are not in the Iwasawa algebra; 2. The p-Selmer group is not cotorsion over the Iwasawa algebra. In this talk, I will explain how to apply the theory of Wach modules to the p-adic representation associated to f under certain conditions to overcome these difficulties. This generalises the works of Pollack and Kobayashi in the most supersingular case.