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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 $p$)".

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Isn't that in the second edition of Washington, cyclotomic fields? –  Joël Oct 20 '12 at 16:29
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up vote 3 down vote accepted

The statement and proof are given in Mazur–Wiles starting at page 216.

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It can also be found in math.clemson.edu/~jimlb/CourseNotes/iwasawa.pdf p. 65ff. –  Timo Keller Oct 20 '12 at 18:16
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