Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales Scientifiques de l'École Normale Supérieure Année : 2004

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

Résumé

We study the degeneration in the Baily–Borel compactification of variations of Hodge structure on Shimura varieties. Our main result, Theorem 2.6, expresses the degeneration of variations given by algebraic representations in terms of Hochschild, and abstract group cohomology. It is the Hodge theoretic analogue of Pink's theorem on degeneration of étale and ℓ-adic sheaves, and completes results by Harder and Looijenga–Rapoport. The induced formula on the level of singular cohomology is equivalent to the theorem of Harris–Zucker on the Hodge structure of deleted neighbourhood cohomology of strata in toroidal compactifications.
Fichier principal
Vignette du fichier
revis.pdf (436.7 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00262303 , version 1 (11-03-2008)

Identifiants

Citer

José Ignacio Burgos, Jörg Wildeshaus. Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification. Annales Scientifiques de l'École Normale Supérieure, 2004, Volume 37 (Issue 3, May-June 2004), pp.363-413. ⟨10.1016/j.ansens.2004.01.002⟩. ⟨hal-00262303⟩
122 Consultations
97 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More