Geodesic
Classical Motivic Polylogarithm According to Beilinson and Deligne
Documenta mathematica, Tome 3 (1998), pp. 27-133
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The main purpose of this paper is the construction in motivic cohomology of the cyclotomic, or classical polylogarithm on the projective line minus three points, and the identi cation of its image under the regulator to absolute (Deligne or l-adic) cohomology. By specialization to roots of unity, one obtains a compatibility statement on cyclotomic elements in motivic and absolute cohomology of abelian number fields. As shown in [BlK], this compatibility completes the proof of the Tamagawa number conjecture on special values of the Riemann zeta function.
DOI : 10.4171/dm/37-5
Classification : 19F27, 11R18, 11R34, 11R42, 14D07, 14F99
Mots-clés : polylogarithm, motivic and absolute cohomology, regulators, cyclotomic elements 
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     author = {Annette Huber and J\"org  Wildeshaus},
     title = {Classical {Motivic} {Polylogarithm} {According} to {Beilinson} and {Deligne}},
     journal = {Documenta mathematica},
     pages = {27--133},
     year = {1998},
     volume = {3},
     doi = {10.4171/dm/37-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/37-5/}
}
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Annette Huber; Jörg  Wildeshaus. Classical Motivic Polylogarithm According to Beilinson and Deligne. Documenta mathematica, Tome 3 (1998), pp. 27-133. doi: 10.4171/dm/37-5

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