An application of a Hodge realization of Bloch-Kriz mixed Tate motives

TL;DR

This paper demonstrates that the Bloch-Kriz category of mixed Tate motives, combined with a Hodge realization, satisfies the properties needed to support Beilinson and Deligne's approach to Zagier's conjecture on special values of Dedekind zeta functions.

Contribution

It establishes that the Bloch-Kriz category with a Hodge realization possesses the necessary properties for the weak version of Zagier's conjecture.

Findings

Confirmed the properties of the Bloch-Kriz category with Hodge realization

Supported the approach to Zagier's conjecture using mixed Tate motives

Provided a framework connecting motives and special values of zeta functions

Abstract

Beilinson and Deligne proved a weak version of Zagier's conjucture on special values of Dedekind zeta functions assuming the existence of a category of mixed Tate motives which has certain properties. We show that Bloch-Kriz category of mixed Tate motives together with a Hodge realization which we constructed has the required properties.