Analogues of character groups for Hilbert Modular Varieties
by
David Helm
Harvard University

The character group of the maximal subtorus of the Jacobian of a modular curve at a prime of semistable reduction has been a useful tool for the study of classical modular forms. We present an interpretation of this character group in terms of vanishing cycles that generalizes to the higher-dimensional Hilbert modular varieties. Moreover, we show how the Jacquet-Langlands correspondence can be understood as a relationship between the character groups for a Hilbert modular variety and a corresponding Shimura curve.

Date received: October 9, 2003