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

Abstract

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.