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

Burgos, José I.; Wildeshaus, Jörg

doi:10.1016/j.ansens.2004.01.002

Burgos, José I. ; Wildeshaus, Jörg

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 3, pp. 363-413.

Zbl

DOI : 10.1016/j.ansens.2004.01.002

@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},
     publisher = {Elsevier},
     volume = {Ser. 4, 37},
     number = {3},
     year = {2004},
     doi = {10.1016/j.ansens.2004.01.002},
     zbl = {1073.14036},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2004.01.002/}
}

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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. http://archive.numdam.org/articles/10.1016/j.ansens.2004.01.002/

Bibliographie
Cité par

[1] Ash A, Mumford D, Rapoport M, Tai Y, Smooth Compactification of Locally Symmetric Varieties, Lie Groups: History, Frontiers and Applications, vol. IV, Math. Sci. Press, 1975. | MR | Zbl

[2] Baily W.L, Borel A, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442-528. | MR | Zbl

[3] Beilinson A.A, On the derived category of perverse sheaves, in: Manin Yu.I (Ed.), K-Theory, Arithmetic and Geometry, Lect. Notes Math., vol. 1289, Springer, Berlin, 1987, pp. 27-41. | MR | Zbl

[4] Beilinson A.A, Bernstein J, Deligne P, Faisceaux pervers, in: Teissier B, Verdier J.-L (Eds.), Analyse et topologie sur les espaces singuliers (I), Astérisque, vol. 100, Soc. Math. France, 1982. | MR | Zbl

[5] Borel A, Serre J.-P, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436-491. | MR | Zbl

[6] Burgos J.I, Wildeshaus J, 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. | MR | Zbl

[7] Cattani E, Kaplan A, Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure, Inv. Math. 67 (1982) 101-115. | MR | Zbl

[8] Cattani E, Kaplan A, Schmid W, Degeneration of Hodge structures, Ann. of Math. 123 (1986) 457-535. | MR | Zbl

[9] Deligne P, Cohomologie à supports propres, in: SGA4_III, Lect. Notes Math., vol. 305, Springer, Berlin, 1973, pp. 250-480. | MR | Zbl

[10] Deligne P, La conjecture de Weil. II, Publ. Math. IHES 52 (1981) 313-428. | Numdam | MR | Zbl

[11] Galligo A, Granger M, Maisonobe P, D-modules et faisceaux pervers dont le support singulier est un croisement normal, Ann. Inst. Fourier (Grenoble) 35 (1985) 1-48. | Numdam | MR | Zbl

[12] Harder G., Eisenstein-Kohomologie arithmetischer Gruppen: Allgemeine Aspekte, Preprint, Bonn, 1986.

[13] Harris M, Zucker S, Boundary cohomology of Shimura varieties II. Hodge theory at the boundary, Inv. Math. 116 (1994) 243-307. | MR | Zbl

[14] Harris M, Zucker S, 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. | Numdam | MR | Zbl

[15] Kashiwara M, A study of variation of mixed Hodge structure, Publ. RIMS, Kyoto Univ. 22 (1986) 991-1024. | MR | Zbl

[16] Kempf G, Knudsen F, Mumford D, Saint-Donat B, Toroidal Embeddings. I, Lect. Notes Math., vol. 339, Springer, Berlin, 1973. | MR | Zbl

[17] Looijenga E, Rapoport M, Weights in the local cohomology of a Baily-Borel compactification, in: Carlson J.A, Clemens C.H, Morrison D.R (Eds.), Complex Geometry and Lie Theory, Proc. of Symp. in Pure Math., vol. 53, Amer. Math. Society, 1991, pp. 223-260. | MR | Zbl

[18] Pink R, Arithmetical Compactification of Mixed Shimura Varieties, Bonner Mathematische Schriften, vol. 209, Univ. Bonn, 1990. | MR | Zbl

[19] Pink R, On ℓ-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification, Math. Ann. 292 (1992) 197-240. | MR | Zbl

[20] Raghunathan M.S, Cohomology of arithmetic subgroups of algebraic groups: I, Ann. of Math. 86 (1967) 409-424. | Zbl

[21] Saito M, Mixed Hodge modules, Publ. RIMS, Kyoto Univ. 26 (1990) 221-333. | MR | Zbl

[22] Schmid W, Variations of Hodge structure: the singularities of the period mapping, Inv. Math. 22 (1973) 211-319. | MR | Zbl

[23] Serre J.-P, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1955-56) 1-42. | Numdam | MR | Zbl

[24] Verdier J.-L, Catégories dérivées, état 0, in: SGA 41/2, Lect. Notes Math., vol. 569, Springer, Berlin, 1977, pp. 262-311. | Zbl

[25] Verdier J.-L, Spécialisation de faisceaux et monodromie modérée, in: Teissier B, Verdier J.-L (Eds.), Analyse et topologie sur les espaces singuliers (II-III), Astérisque, vol. 101-102, Soc. Math. France, 1982, pp. 332-364. | Numdam | MR | Zbl

[26] Verdier J.-L, Extension of a perverse sheaf over a closed subspace, in: Galligo A, Granger M, Maisonobe P (Eds.), Systèmes différentiels et singularités, Astérisque, vol. 130, Soc. Math. France, 1985, pp. 210-217. | Numdam | MR | Zbl

[27] Vogan D.A, Representations of Real Reductive Lie Groups, Prog. in Math., vol. 15, Birkhäuser, Basel, 1981. | MR | Zbl

[28] Wildeshaus J, 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] Wildeshaus J, Mixed sheaves on Shimura varieties and their higher direct images in toroidal compactifications, J. Algebraic Geom. 9 (2000) 323-353. | MR | Zbl

[30] Wildeshaus J, On derived functors on categories without enough injectives, J. Pure Appl. Algebra 150 (2000) 207-213. | MR | Zbl

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