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

Understand

In this paper, we construct a higher rank Euler system for the multiplicative group over a totally real field by using the Iwasawa main conjecture proved by Wiles.

• A key ingredient of the construction is to generalize the notion of the characteristic ideal.
• Under certain technical assumptions, we prove that all higher Fitting ideals of a certain $p$-ramified Iwasawa module are described by analytic invariants canonically associated with Stickelberger elements.