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

TL;DR

This paper develops a new framework in Iwasawa theory for Tate motives over totally real fields, constructing zeta elements that interpolate L-values and linking them to Galois cohomology, advancing understanding of special values and functional equations.

Contribution

It introduces a novel construction of zeta elements for Tate motives over totally real fields, connecting L-values with Galois cohomology in a new way.

Findings

Construction of zeta elements interpolating L-values

Canonical elements in Galois cohomology related to L-values

Advancement in understanding functional equations for Tate motives

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.