Classical Polylogarithm -- Abstract of a series of lectures given at the workshop on polylogs in Essen, May 1 -- 4, 1997

TL;DR

This paper discusses the construction of the motivic polylogarithm, focusing on its Hodge theoretic aspects, and highlights its application in comparing cyclotomic elements relevant to the Tamagawa number conjecture.

Contribution

It provides an exposition of the motivic polylogarithm construction and its role in the proof of the Tamagawa number conjecture for Dirichlet characters.

Findings

Construction of the motivic polylogarithm explained

Comparison result for cyclotomic elements established

Application to Tamagawa number conjecture demonstrated

Abstract

These are extended abstracts from an series of lectures in 1997. The text has not been updated since then. We explain the construction of the motivic polylog as published in Annette Huber, J\"org Wildeshaus, Classical Motivic Polylogarithm According to Beilinson and Deligne, Doc.Math.J.DMV 3 (1998) 27-133. The main application is a comparison result for cyclotomic elements needed in the proof of the Tamagawa number conjecture of Bloch and Kato for Dirichlet characters. The exposition concentrates on the Hodge theoretic part of the story.