I need a reference/proof for "main conjecture of Iwasawa theory => refinement of Herbrand-Ribet ($v\_p(B\_{p-i}) = v\_p(|A\_i|)$, where $A\_i$ denotes the $i$-th eigenspace of the Galois group acting on the ideal class group mod $p$)".



main conjecture of Iwasawa theory implies Herbrand-Ribet
The statement and proof are given in Mazur–Wiles starting at page 216.


