Selmer groups and the Eisenstein-Klingen ideal

In this paper we set up a strategy to prove one divisibility toward the mai n Iwasawa conjecture for the Selmer groups attached to the twisted adjoint modular Galois representations associated to Hida families. This conjecture asserts the equality of the p-adic L-function interpolating the critical v alues of the symmetric square of the modular forms in these families and th e characteristic ideal of the associated Selmer group, The idea is to intro duce a third characteristic ideal containing information on the congruences between cuspidal Siegel modular forms of genus 2 and the Klingen-type Eise nstein series and to prove the two divisibilities: the p-adic L-function di vides the Eisenstein ideal, and the Eisenstein ideal divides the characteri stic ideal of the Selmer group. We prove the latter divisibility in this pa per which is an improved version of the old preprint http://www.math.uiuc.e du/Algebraic-Number Theory/0107/index.html.