Classical Motivic Polylogarithm according to Beilinson and Deligne, by A. Huber and J. Wildeshaus

Based on the unpublished preprint [BD] of Beilinson and Deligne, we give the construction of the classical polylogarithm in the motivic cohomology of a certain simplicial scheme and compute its regulators in absolute Hodge and etale cohomology.

As a consequence, we obtain an alternative proof of Beilinson's theorem on the regulator of the cyclotomic elements in the K-theory of an abelian number field.

Another consequence is the validity of Conjecture 6.2 of [BK], and hence, of the Tamagawa number conjecture for Tate twists up to powers of two, also for twists of odd parity.

[BD] A.A. Beilinson, P. Deligne, ``Motivic Polylogarithm and Zagier Conjecture'', preprint, 1992.

[BK] S. Bloch, K. Kato, ``L-functions and Tamagawa numbers of Motives'', The Grothendieck Festschrift, Volume I.

A. Huber <>
J. Wildeshaus <>