Realizations of Polylogarithms

Jörg Wildeshaus (auth.)3540624600, 9783540624608

Classically, higher logarithms appear as multivalued functions on the projective line. Today they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the “polylogarithm”. The aim of the book is to document the sheaf-theoretical foundations of the field of polylogarithms. Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties. The reader is expected to have a sound background in algebraic geometry. Large parts of the book are expository, and intended as a reference for the working mathematician. Where a self-contained exposition was not possible, the author gives references in order to make the material accessible for advanced graduate students.

---

Table of contents :
Introduction….Pages 1-21
Mixed structures on fundamental groups….Pages 23-76
The canonical construction of mixed sheaves on mixed shimura varieties….Pages 77-140
Polylogarithmic extensions on mixed shimura varieties. Part I: Construction and basic properties….Pages 141-197
Polylogarithmic extensions on mixed shimura varieties. part II: The classifical polylogarithm….Pages 199-248
Polygogarithmic extensions on mixed shimura varieties. Part III: The elliptic polygogarithm….Pages 249-335