Realizations of Polylogarithms

Jörg Wildeshaus (Autor)

Buch | Softcover

XII, 344 Seiten

1997 | 1997
Springer Berlin (Verlag)
978-3-540-62460-8 (ISBN)

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 Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties.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

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.

Erscheint lt. Verlag	20.2.1997
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 344 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	467 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Algebra • Algebraic Geometry • Grad • logarithm • Logarithmen • polylogarithms • realization
ISBN-10	3-540-62460-0 / 3540624600
ISBN-13	978-3-540-62460-8 / 9783540624608
Zustand	Neuware