Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification
Abstract
We prove an analogue for Hodge modules of Pink's theorem on the degeneration of l-adic sheaves (Math. Ann. 292). Let j be the open immersion of a Shimura variety M into its Baily-Borel compactification. Its boundary has a natural stratification into locally closed subsets, each of which is itself a Shimura variety (up to taking the quotient by the action of a finite group). Let i be the inclusion of an individual such stratum M'. Saito's formalism gives a functor i^* j_* from the bounded derived category of Hodge modules on M to that of Hodge modules on M'. Our result gives a formula for the effect of i^* j_* on automorphic Hodge modules, i.e., variations of Hodge structure coming from algebraic representations of the group associated to M. This formula is of a purely representation theoretical nature.
Keywords
Cite
@article{arxiv.math/0209370,
title = {Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification},
author = {J. I. Burgos and J. Wildeshaus},
journal= {arXiv preprint arXiv:math/0209370},
year = {2007}
}
Comments
62 pages; the present version of the article is the slightly modified and final version of preprint no. math.AG/0209370. It will appear in Ann. scient. ENS