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

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1. [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. Zbl0334.14007MR457437
2. [2] Baily W.L, Borel A, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math.84 (1966) 442-528. Zbl0154.08602MR216035
3. [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. Zbl0652.14008MR923133
4. [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. Zbl0536.14011MR751966
5. [5] Borel A, Serre J.-P, Corners and arithmetic groups, Comment. Math. Helv.48 (1973) 436-491. Zbl0274.22011MR387495
6. [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. Paris336 (2003) 29-34. Zbl1051.14026MR1968898
7. [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. Zbl0516.14005MR664326
8. [8] Cattani E, Kaplan A, Schmid W, Degeneration of Hodge structures, Ann. of Math.123 (1986) 457-535. Zbl0617.14005MR840721
9. [9] Deligne P, Cohomologie à supports propres, in: SGA4III, Lect. Notes Math., vol. 305, Springer, Berlin, 1973, pp. 250-480. Zbl0255.14011MR354654
10. [10] Deligne P, La conjecture de Weil. II, Publ. Math. IHES52 (1981) 313-428. Zbl0456.14014MR601520
11. [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. Zbl0572.32012MR781776
12. [12] Harder G., Eisenstein-Kohomologie arithmetischer Gruppen: Allgemeine Aspekte, Preprint, Bonn, 1986. 
13. [13] Harris M, Zucker S, Boundary cohomology of Shimura varieties II. Hodge theory at the boundary, Inv. Math.116 (1994) 243-307. Zbl0860.11031MR1253194
14. [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. Zbl1020.11042MR1850830
15. [15] Kashiwara M, A study of variation of mixed Hodge structure, Publ. RIMS, Kyoto Univ.22 (1986) 991-1024. Zbl0621.14007MR866665
16. [16] Kempf G, Knudsen F, Mumford D, Saint-Donat B, Toroidal Embeddings. I, Lect. Notes Math., vol. 339, Springer, Berlin, 1973. Zbl0271.14017MR335518
17. [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. Zbl0753.14016MR1141203
18. [18] Pink R, Arithmetical Compactification of Mixed Shimura Varieties, Bonner Mathematische Schriften, vol. 209, Univ. Bonn, 1990. Zbl0748.14007MR1128753
19. [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. Zbl0748.14008MR1149032
20. [20] Raghunathan M.S, Cohomology of arithmetic subgroups of algebraic groups: I, Ann. of Math.86 (1967) 409-424. Zbl0157.06802
21. [21] Saito M, Mixed Hodge modules, Publ. RIMS, Kyoto Univ.26 (1990) 221-333. Zbl0727.14004MR1047415
22. [22] Schmid W, Variations of Hodge structure: the singularities of the period mapping, Inv. Math.22 (1973) 211-319. Zbl0278.14003MR382272
23. [23] Serre J.-P, Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier6 (1955–56) 1-42. Zbl0075.30401MR82175
24. [24] Verdier J.-L, Catégories dérivées, état 0, in: SGA 41/2, Lect. Notes Math., vol. 569, Springer, Berlin, 1977, pp. 262-311. Zbl0407.18008
25. [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. Zbl0532.14008MR737938
26. [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. Zbl0572.14011MR804054
27. [27] Vogan D.A, Representations of Real Reductive Lie Groups, Prog. in Math., vol. 15, Birkhäuser, Basel, 1981. Zbl0469.22012MR632407
28. [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. MR1482233
29. [29] Wildeshaus J, Mixed sheaves on Shimura varieties and their higher direct images in toroidal compactifications, J. Algebraic Geom.9 (2000) 323-353. Zbl0956.14017MR1735776
30. [30] Wildeshaus J, On derived functors on categories without enough injectives, J. Pure Appl. Algebra150 (2000) 207-213. Zbl0966.18008MR1765871