@article{ASENS_2004_4_37_3_363_0,
author = {Burgos, Jos\'e I. and Wildeshaus, J\"org},
title = {Hodge modules on {Shimura} varieties and their higher direct images in the {Baily-Borel} compactification},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {363--413},
year = {2004},
publisher = {Elsevier},
volume = {Ser. 4, 37},
number = {3},
doi = {10.1016/j.ansens.2004.01.002},
zbl = {1073.14036},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2004.01.002/}
}
TY - JOUR AU - Burgos, José I. AU - Wildeshaus, Jörg TI - Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification JO - Annales scientifiques de l'École Normale Supérieure PY - 2004 SP - 363 EP - 413 VL - 37 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2004.01.002/ DO - 10.1016/j.ansens.2004.01.002 LA - en ID - ASENS_2004_4_37_3_363_0 ER -
%0 Journal Article %A Burgos, José I. %A Wildeshaus, Jörg %T Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification %J Annales scientifiques de l'École Normale Supérieure %D 2004 %P 363-413 %V 37 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2004.01.002/ %R 10.1016/j.ansens.2004.01.002 %G en %F ASENS_2004_4_37_3_363_0
Burgos, José I.; Wildeshaus, Jörg. Hodge modules on Shimura varieties and their higher direct images in the Baily-Borel compactification. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 3, pp. 363-413. doi: 10.1016/j.ansens.2004.01.002
[1] , , , , Smooth Compactification of Locally Symmetric Varieties, Lie Groups: History, Frontiers and Applications, vol. IV, Math. Sci. Press, 1975. | Zbl | MR
[2] , , Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442-528. | Zbl | MR
[3] , On the derived category of perverse sheaves, in: (Ed.), K-Theory, Arithmetic and Geometry, Lect. Notes Math., vol. 1289, Springer, Berlin, 1987, pp. 27-41. | Zbl | MR
[4] , , , Faisceaux pervers, in: , (Eds.), Analyse et topologie sur les espaces singuliers (I), Astérisque, vol. 100, Soc. Math. France, 1982. | Zbl | MR
[5] , , Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436-491. | Zbl | MR
[6] , , Modules de Hodge sur les variétés de Shimura, et leur dégénérescence dans la compactification de Baily-Borel, C. R. Acad. Sci. Paris 336 (2003) 29-34. | Zbl | MR
[7] , , Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure, Inv. Math. 67 (1982) 101-115. | Zbl | MR
[8] , , , Degeneration of Hodge structures, Ann. of Math. 123 (1986) 457-535. | Zbl | MR
[9] , Cohomologie à supports propres, in: SGA4III, Lect. Notes Math., vol. 305, Springer, Berlin, 1973, pp. 250-480. | Zbl | MR
[10] , La conjecture de Weil. II, Publ. Math. IHES 52 (1981) 313-428. | Zbl | MR | Numdam
[11] , , , D-modules et faisceaux pervers dont le support singulier est un croisement normal, Ann. Inst. Fourier (Grenoble) 35 (1985) 1-48. | Zbl | MR | Numdam
[12] Harder G., Eisenstein-Kohomologie arithmetischer Gruppen: Allgemeine Aspekte, Preprint, Bonn, 1986.
[13] , , Boundary cohomology of Shimura varieties II. Hodge theory at the boundary, Inv. Math. 116 (1994) 243-307. | Zbl | MR
[14] , , Boundary Cohomology of Shimura Varieties III. Coherent Cohomology on Higher-Rank Boundary Strata and Applications to Hodge Theory, Mémoires de la SMF, vol. 85, Soc. Math. France, 2001. | Zbl | MR | Numdam
[15] , A study of variation of mixed Hodge structure, Publ. RIMS, Kyoto Univ. 22 (1986) 991-1024. | Zbl | MR
[16] , , , , Toroidal Embeddings. I, Lect. Notes Math., vol. 339, Springer, Berlin, 1973. | Zbl | MR
[17] , , Weights in the local cohomology of a Baily-Borel compactification, in: , , (Eds.), Complex Geometry and Lie Theory, Proc. of Symp. in Pure Math., vol. 53, Amer. Math. Society, 1991, pp. 223-260. | Zbl | MR
[18] , Arithmetical Compactification of Mixed Shimura Varieties, Bonner Mathematische Schriften, vol. 209, Univ. Bonn, 1990. | Zbl | MR
[19] , On ℓ-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification, Math. Ann. 292 (1992) 197-240. | Zbl | MR
[20] , Cohomology of arithmetic subgroups of algebraic groups: I, Ann. of Math. 86 (1967) 409-424. | Zbl
[21] , Mixed Hodge modules, Publ. RIMS, Kyoto Univ. 26 (1990) 221-333. | Zbl | MR
[22] , Variations of Hodge structure: the singularities of the period mapping, Inv. Math. 22 (1973) 211-319. | Zbl | MR
[23] , Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1955-56) 1-42. | Zbl | MR | Numdam
[24] , Catégories dérivées, état 0, in: SGA 41/2, Lect. Notes Math., vol. 569, Springer, Berlin, 1977, pp. 262-311. | Zbl
[25] , Spécialisation de faisceaux et monodromie modérée, in: , (Eds.), Analyse et topologie sur les espaces singuliers (II-III), Astérisque, vol. 101-102, Soc. Math. France, 1982, pp. 332-364. | Zbl | MR | Numdam
[26] , Extension of a perverse sheaf over a closed subspace, in: , , (Eds.), Systèmes différentiels et singularités, Astérisque, vol. 130, Soc. Math. France, 1985, pp. 210-217. | Zbl | MR | Numdam
[27] , Representations of Real Reductive Lie Groups, Prog. in Math., vol. 15, Birkhäuser, Basel, 1981. | Zbl | MR
[28] , The canonical construction of mixed sheaves on mixed Shimura varieties, in: Realizations of Polylogarithms, Lect. Notes Math., vol. 1650, Springer, Berlin, 1997, pp. 77-140. | MR
[29] , Mixed sheaves on Shimura varieties and their higher direct images in toroidal compactifications, J. Algebraic Geom. 9 (2000) 323-353. | Zbl | MR
[30] , On derived functors on categories without enough injectives, J. Pure Appl. Algebra 150 (2000) 207-213. | Zbl | MR
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