Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification

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dc.creatorBurgos, J. I.
dc.creatorWildeshaus, J.
dc.date2002-09-26
dc.date2004-01-07
dc.date.accessioned2026-07-07T08:27:19Z
dc.date.available2026-07-07T08:27:19Z
dc.descriptionWe 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.
dc.description62 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
dc.identifierhttps://arxiv.org/abs/math/0209370
dc.identifierhttp://arxiv.org/abs/math/0209370
dc.identifierAnn. Scient. Ec. Norm. Sup. 37 (2004), 363-413
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137234
dc.subjectAlgebraic Geometry
dc.subject14G35 (11F75; 14D07; 14F25; 14F40; 14F43; 32G20)
dc.titleHodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification
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