Realizations of polylogarithms
著者
書誌事項
Realizations of polylogarithms
（Lecture notes in mathematics, 1650）
Springer-Verlag, c1997
大学図書館所蔵 全87件
注記
Includes indexes of notations and bibliographies at each end of chapters, and index at end of volume
内容説明・目次
内容説明
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 Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties.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.
目次
Mixed structures on fundamental groups.- The canonical construction of mixed sheaves on mixed shimura varieties.- Polylogarithmic extensions on mixed shimura varieties. Part I: Construction and basic properties.- Polylogarithmic extensions on mixed shimura varieties. part II: The classifical polylogarithm.- Polygogarithmic extensions on mixed shimura varieties. Part III: The elliptic polygogarithm.
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