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- W2158407811 abstract "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 [Math. Ann. 292 (1992) 197], and completes results by Harder and Looijenga–Rapoport [Eisenstein-Kohomologie arithmetischer Gruppen: Allgemeine Aspekte, Preprint, 1986; Proc. of Symp. in Pure Math., vol. 53, 1991, pp. 223–260]. 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 [Inv. Math. 116 (1994) 243]. Ce travail concerne la dégénérescence des variations de structure de Hodge sur les variétés de Shimura. Le résultat principal, le théorème 2.6, exprime cette dégénérescence en termes de cohomologie de Hochschild, et de cohomologie abstraite des groupes. Ce résultat est l'analogue, en théorie de Hodge, du théorème de Pink sur la dégénérescence des faisceaux étales et ℓ-adiques [Math. Ann. 292 (1992) 197], et complète des résultats obtenus par Harder et Looijenga–Rapoport [Eisenstein-Kohomologie arithmetischer Gruppen : Allgemeine Aspekte, Preprint, 1986 ; Proc. of Symp. in Pure Math., vol. 53, 1991, pp. 223–260]. Il induit une formule au niveau de la cohomologie singulière, qui est équivalente au théorème de Harris–Zucker concernant la structure de Hodge sur la “deleted neighbourhood cohomology” des strates des compactifications toroı̈dales [Inv. Math. 116 (1994) 243]." @default.
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- W2158407811 date "2004-05-01" @default.
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- W2158407811 title "Hodge modules on Shimura varieties and their higher direct images in the Baily–Borel compactification" @default.
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- W2158407811 doi "https://doi.org/10.1016/j.ansens.2004.01.002" @default.
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