On zeta elements and functional equations for Tate motives over totally real fields

In this paper, we study Iwasawa theory for Tate motives over totally real fields. More precisely, we construct a zeta element that interpolates the values of $L$-functions at positive integers over totally real fields under a certain unramified condition at $p$. As an application of this, we construct a canonical element in the exterior power bidual of the Galois cohomology group that is also related to the values of $L$-functions at positive integers.