ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: Wildeshaus, Jörg, Univ. of Münster Degeneration of Shimura Polylogarithms Generalizing the sheaf theoretic approach to polylogarithms of Beilinson, Deligne and Levin to the context of Shimura varieties, one can ask about the behaviour of this notion with respect to geometric constructions one can perform on the level of the varieties. According to Pink, one may choose toroidal compactifications of a Shimura variety in such a way that the boundary possesses a stratification into smaller Shimura varieties. We show that the concept of polylog is in a precise sense stable under degeneration into such a toroidal compactification.