The Bloch-Kriz category of mixed Tate motives over a number field, with the author's Hodge realization, satisfies Beilinson-Deligne's conditions (A) through (E), yielding a weak form of Zagier's conjecture.
and Kriz, I., Mixed Tate Motives , Ann
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An application of a Hodge realization of Bloch-Kriz mixed Tate motives
The Bloch-Kriz category of mixed Tate motives over a number field, with the author's Hodge realization, satisfies Beilinson-Deligne's conditions (A) through (E), yielding a weak form of Zagier's conjecture.