Le syst\`eme d'Euler de Kato en famille (II)

Abstract

This article is the second article on the generalization of Kato's Euler system. The main subject of this article is to construct a family of Kato's Euler systems over the cuspidal eigencurve, which interpolate the Kato's Euler systems associated to the modular forms parametrized by the cuspidal eigencurve. We also explain how to use this family of Kato's Euler system to construct a family of distributions on $Z_p$ over the cuspidal eigencurve; this distribution gives us a two variable $p$-adic L function which interpolate the $p$-adic L function of modular forms.