By Jörg Wildeshaus

Classically, greater logarithms seem as multivalued features at the projective line. at the present time they are often interpreted as entries of the interval matrix of a definite edition of Hodge constitution, itself known as the "polylogarithm". the purpose of the booklet is to record the sheaf-theoretical foundations of the sphere of polylogarithms. past, in part unpublished effects and structures of Beilinson, Deligne, and Levin at the classical and elliptic polylog are generalized to the context of Shimura types. The reader is predicted to have a valid heritage in algebraic geometry. huge elements of the booklet are expository, and meant as a reference for the operating mathematician. the place a self-contained exposition used to be impossible, the writer supplies references with a purpose to make the cloth available for complex graduate scholars.

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