Realizations of Polylogarithms: 1650 (Lecture Notes in Mathematics, 1650) - Softcover

Wildeshaus, Jörg

Softcover

ISBN 10: 3540624600 ISBN 13: 9783540624608

Publisher: Springer, 1997

Synopsis

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 Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties.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.

About this title

Synopsis

Classically, higher logarithms appear as multivalued fuction on the projective line. More recently they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm". Documenting the sheaf-theoretical foundations of the field of polylogarithms, this text assumes a sound background in algebraic geometry. Large parts of the text are intended as a reference for the working mathematician. Where a self-contained explanation was not possible, the author gives references in order to make the material accessible for advanced graduate students.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 3540624600
• ISBN 13: 9783540624608
• Binding: Paperback
• Number of pages: 356