@article{CM_1986__60_3_323_0, author = {Harris, Michael}, title = {Arithmetic vector bundles and automorphic forms on {Shimura} varieties, {II}}, journal = {Compositio Mathematica}, pages = {323--378}, publisher = {Martinus Nijhoff Publishers}, volume = {60}, number = {3}, year = {1986}, mrnumber = {869106}, zbl = {0612.14019}, language = {en}, url = {http://archive.numdam.org/item/CM_1986__60_3_323_0/} }
TY - JOUR AU - Harris, Michael TI - Arithmetic vector bundles and automorphic forms on Shimura varieties, II JO - Compositio Mathematica PY - 1986 SP - 323 EP - 378 VL - 60 IS - 3 PB - Martinus Nijhoff Publishers UR - http://archive.numdam.org/item/CM_1986__60_3_323_0/ LA - en ID - CM_1986__60_3_323_0 ER -
Harris, Michael. Arithmetic vector bundles and automorphic forms on Shimura varieties, II. Compositio Mathematica, Tome 60 (1986) no. 3, pp. 323-378. http://archive.numdam.org/item/CM_1986__60_3_323_0/
[1] Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442-528. | MR | Zbl
and :[5] Travaux de Shimura. Sém. Bourbaki 23 (1970/71) No. 389. | Numdam | MR | Zbl
:[6] Variétés de Shimura: Interprétation modulaire, et techniques de construction des modèles canoniques. Proc. Symp. Pure Math. XXXIII (1979) Part 2, 247-290. | MR | Zbl
:[11] Arithmetic and structure of automorphic forms on bounded symmetric domains. Am. J. Math., 105 (1983) 1171-1194; II, Ibid., 1195-1216. | MR | Zbl
:[12] Eisenstein series on Shimura varieties. Ann. of Math., 119 (1984). | MR | Zbl
:[13] Arithmetic vector bundles on Shimura varieties, in A utomorphic Forms of Several Variables, Progress in Math. (Boston: Birkhäuser-Verlag) (1984). | MR | Zbl
:[19] On canonical models of arithmetic quotients of bounded symmetric domains I, II. Ann. of Math. 91 (1970) 144-222; 92 (1970) 528-549. | MR | Zbl
:[20] On certain reciprocity laws for theta functions and modular forms. Acta Math. 141 (1978) 35-71. | MR | Zbl
:[21] The arithmetic of automorphic forms with respect to a unitary group. Ann. of Math. 107 (1978) 569-605. | MR | Zbl
:[23] Automorphic forms and the periods of abelian varieties. J. Math. Soc. Japan 31 (1979) 561-592. | MR | Zbl
:[24] The arithmetic of certain zeta functions and automorphic forms on orthogonal groups. Ann. of Math. 111 (1980) 313-375. | MR | Zbl
:[26] Smooth Compactification of Locally Symmetric Varieties, Brookline, Mass.: Math. Sci. Press (1975). | MR | Zbl
; , , and :[27] Jr.: On the Fourier coefficients of certain Eisenstein series on the adèle group. In: Number Theory, Algebraic Geometry, and Commutative Algebra: in Honor of Y. Akizuki, Tokyo: Kinokuniya (1973). | MR | Zbl
,[28] Arithmetic of monomial relations between the periods of abelian varieties. Thesis, Princeton University (1981).
:[29] L2-cohomology and intersection cohomology of certain arithmetic varieties. In B. Srinivasan and J. Sally (eds) Emmy Noether in Bryn Mawr. New York: Springer-Verlag (1983) 119-131. | MR | Zbl
:[30] Groupes Rèductifs. Publ. Math. I.H.E.S. 27 (1965) 55-151. | Numdam | MR | Zbl
and :[31] "1-motifs" et formes automorphes. In Journées Automorphes, Publ. Math. de l'Univ. Paris VII 15 (1983). | MR | Zbl
:[32] Compactifications of Siegel Moduli Schemes, Cambridge: Cambridge University Press (1985). | MR | Zbl
:[33] Limit formulas for multiplicities in L2(Γ\G). Ann. of Math. 107 (1978) 133-150. | Zbl
and :[34] Espaces Hermitiens symétriques, notes from a course at I.H.E.S.
:[35] Les schémas de modules de courbes elliptiques. Lecture Notes in Math 349 (1972) 143-316. | MR | Zbl
and :[36] Modular curves on arithmetic quotients. Duke Math. J. 49 (1982) 633-654. | MR | Zbl
:[37] Special values of zeta functions attached to Siegel modular forms. Ann. Sci. de l'E.N.S. 14 (1981) 77-120. | Numdam | MR | Zbl
:[38] Maass operators and Eisenstein series. Math. Ann. 258 (1981) 135-144. | MR | Zbl
:[39] Fourier coefficients of non-holomorphic Eisenstein series on a tube domain associated to an orthogonal group, to appear.
:[40] Restrictions and expansions of holomorphic representations, J. Fun. Analysis 34, (1979) 29-53. | MR | Zbl
and :[41] p-adic L-functions for CM fields. Inv. Math. 59 (1978) 199-297. | MR | Zbl
:[42] On certain arithmetic automorphic forms for SU(1, q). Inv. Math. 52 (1979) 1-26. | MR | Zbl
:[43] Siegel's Modular Forms and Dirichlet Series, Lecture Notes in Math., 216 (1971). | Zbl
:[44] On the equations defining abelian varieties: I, II, III, Inv. Math. 1 (1966) 287-354; 3 (1967) 75-135, 215-244. | MR | Zbl
:[45] On modular forms associated with indefinite quadratic forms of signature (2, n - 2), Math. Ann. 231 (1977) 97-144. | MR | Zbl
:[46] Hodge structures of Shimura varieties attached to the unit groups of quaternion algebras, in Advanced Studies in Pare Mathematics 2: Galois Groups and Their Representations, 15-36 Tokyo: Kinokuniya Press (1983). | MR | Zbl
:[47] Geometry of Classical Domains and the Theory of Automorphic Functions, New York, Gordon and Breach (1969).
:[48] L-functions for the classical groups, notes on a seminar at I.A.S. prepared by (1984).
and :[49] Algebraic Structures of Symmetric Domains, Princeton University Press (1980). | MR | Zbl
:[50] On a conjecture of Langlands. Ann. of Math. 93 (1971) 1-42. | MR | Zbl
:[51] Dissertation, Berlin (1901).
:[52] Modules des variétés abéliennes polarisées et fonctions modulaires: I, II, III, In Sém. Cartan 1957/58, exposés 18-20, New York: Benjamin (1967). | Numdam
:[53] On some arithmetic properties of modular forms of one and several variables. Ann. of Math. 102 (1975) 491-515. | MR | Zbl
:[54] On the Fourier coefficients of modular forms of several variables. Göttinger Nachr. Akad. Wiss. Nr. 17 (1975) 261-268. | MR | Zbl
:[55] The special values of the zeta functions associated with cusp forms. Comm. Pure Appl. Math. 29 (1976) 783-804. | MR | Zbl
:[56] On certain zeta functions attached to two Hilbert modular forms: I, II. Ann. of Math. 114 (1981) 127-164, 569-607. | Zbl
:[57] Arithmetic of differential operators on symmetric domains. Duke Math. J. 48 (1981) 813-843. | MR | Zbl
:[58] Algebraic relations between critical values of zeta functions and inner products. Am. J. Math. 105 (1983) 253-285. | MR | Zbl
:[59] On Eisenstein series, Duke Math. J. 50 (1983) 417-476. | MR | Zbl
:[60] The rationality of the Fourier coefficients of certain Eisenstein series on tube domains. Compositio Math. 32 (1976) 225-291. | Numdam | MR | Zbl
:[61] Analytic continuation of holomorphic discrete series. A cta Math. 136 (1976) 1-59. | MR | Zbl
and :[62] Analytic continuation of the discrete series II. Trans. A.M.S. 251 (1979) 19-37. | MR | Zbl
:[63] Sur les coefficients de Fourier des formes modulaires de poids demi-en-tier. J. Math. pures et appl. 60 (1981) 375-484. | MR | Zbl
:[64] Correspondances de Shimura et quaternions, preprint (1983). | MR | Zbl
:[65] Fine structure of Hermitian symmetric spaces. In: Symmetric Spaces Short Lectures, pp. 271-357, New York: Dekker (1972). | MR | Zbl
:[66] Generalized Cayley transformations of bounded symmetric domains. Am. J. Math. 87 (1965) 899-939. | MR | Zbl
and :[67] L2-cohomology of warped products and arithmetic groups. Inv. Math. 70 (1982) 169-218. | MR | Zbl
:[68] L2-cohomology and intersection homology of locally symmetric varieties, II, preprint (1983).
:[69] Théorie de Hodge, II, Publ. Math. I.H.E.S. 40 (1971) 5-58. | Numdam | MR | Zbl
:[70] On limit multiplicities of discrete series representations in spaces of automorphic forms Inv. Math. 83 (1986) 265-284. | MR | Zbl
:[71] Arithmetische Kompaktifizierung des Modulraums der abelschen Varietäten. In Arbeitstagung Bonn 1984, Lect. Notes in Math. 1111 (1985) 321-383. | MR | Zbl
:[72] Arithmetic vector bundles and automorphic forms on Shimura varieties, I. Inv. Math. 82 (1985) 151-189. | MR | Zbl
:[73] Automorphic forms of discrete type as coherent cohomology classes (preprint). | MR
: