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For a finite abelian -extension of totally real fields and the cyclotomic -extension , we prove a strong version of an equivariant Iwasawa main conjecture by determining completely the Fitting ideal over of the classical Iwasawa module , which is the Galois group of the maximal pro- abelian -ramified extension of , where contains all ramified primes in . To do this, we prove a conjecture which was proposed in a previous paper by the first and second author, concerning the minors of a relation matrix for the second syzygy module of the trivial module over a suitable group ring.
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Published: 1 January 2020
First available in Project Euclid: 12 January 2021