I would like to read and understand the Mazur-Wiles paper on Iwasawa theory: "Class Fields of Abelian Extensions of $\Bbb Q$". What would be the right way to approach this paper?

Currently, my background is as follows: I know a fair bit of algebraic geometry (equivalent to Hartshorne), Class Field Theory (Milne's notes), Elliptic Curves (Silverman's two books) and the basic theory of Modular forms (Diamond and Shurman) and have read parts of Washington's book "Cyclotomic Fields".

I am currently in the middle of reading about modular forms mod p through Serre's papers in the Antwerp volume ("Formes modulaires et fonctions zêta p-adiques"). I have also gone through Ribet's paper on Herbrand-Ribet.

Is this sufficient background to read the Mazur-Wiles paper? I feel like I lack some background on the reduction of modular curves - this was the only part of Ribet's paper that I couldn't follow.

I would also be interested in surveys of the paper if there are any.

$p$-adic properties of modular schemes and modular forms, which is in the Antwerp volume (and I thought it was the appendix of the volume); the (first) appendix of Katz' paper is the link with classical complex modular forms, and (although very interesting in its own) probably not strictly necessary—but if you digest the whole paper, Appendix 1 will come for free as an easy final reading. Concerning Serre: beautifully written, technically Katz contains it but the main idea beneath Katz' paper is to "understand geometrically" Serre's. Read it, Katz will become easier. $\endgroup$