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

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.