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In this paper, we construct a higher rank Euler system for the multiplicativegroup over a totally real field by using the Iwasawa main conjecture proved byWiles. A key ingredient of the construction is to generalize the notion of thecharacteristic ideal. Under certain technical assumptions, we prove that allhigher Fitting ideals of a certain $p$-ramified Iwasawa module are described byanalytic invariants canonically associated with Stickelberger elements.

A higher rank Euler system for the multiplicative group over a totally real field