Duke Mathematical Journal

Algebraic cycles on Shimura varieties of orthogonal type

Stephen S. Kudla

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Duke Math. J. Volume 86, Number 1 (1997), 39-78.

First available in Project Euclid: 19 February 2004

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Zentralblatt MATH identifier

Primary: 11F32: Modular correspondences, etc.
Secondary: 11F30: Fourier coefficients of automorphic forms 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14C25: Algebraic cycles 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]


Kudla, Stephen S. Algebraic cycles on Shimura varieties of orthogonal type. Duke Math. J. 86 (1997), no. 1, 39--78. doi:10.1215/S0012-7094-97-08602-6. https://projecteuclid.org/euclid.dmj/1077242496

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  • [1] Avner Ash, Nonminimal modular symbols for $\rm GL(n)$, Invent. Math. 91 (1988), no. 3, 483–491.
  • [2] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura, J. Reine Angew. Math. 430 (1992), 69–83.
  • [3] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura. II. Calculs et applications, J. Reine Angew. Math. 444 (1993), 1–15.
  • [4] L. Clozel and T. N. Venkataramana, Restriction of holomorphic cohomology of a Shimura variety to a smaller Shimura variety, preprint, 1996.
  • [5] S. Gelbart, J. Rogawski, and D. Soudry, On periods of cusp forms and algebraic cycles for $\rm U(3)$, Israel J. Math. 83 (1993), no. 1-2, 213–252.
  • [6] S. Gelbart, J. Rogawski, and D. Soudry, Periods of cusp forms and $L$-packets, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 8, 717–722.
  • [7] S. Gelbart, J. Rogawski, and D. Soudry, Endoscopy and theta liftings for unitary groups in three variables, preprint, 1994.
  • [8] B. Gross and K. Keating, On the intersection of modular correspondences, Invent. Math. 112 (1993), no. 2, 225–245.
  • [9] B. Gross and S. Kudla, Heights and the central critical values of triple product $L$-functions, Compositio Math. 81 (1992), no. 2, 143–209.
  • [10] G. Harder, Period integrals of Eisenstein cohomology classes and special values of some $L$-functions, Number Theory Related to Fermat's Last Theorem (Cambridge, Mass., 1981), Progr. Math., vol. 26, Birkhäuser, Boston, 1982, pp. 103–142.
  • [11] G. Harder, R. P. Langlands, and M. Rapoport, Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366 (1986), 53–120.
  • [12] M. Harris and S. Kudla, The central critical value of a triple product $L$-function, Ann. of Math. (2) 133 (1991), no. 3, 605–672.
  • [13] F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math. 36 (1976), 57–113.
  • [14] M. Kneser, Darstellungsmasse indefiniter quadratischer Formen, Math. Z. 77 (1961), 188–194.
  • [15] S. Kudla, Intersection numbers for quotients of the complex $2$-ball and Hilbert modular forms, Invent. Math. 47 (1978), no. 2, 189–208.
  • [16] S. Kudla, Central derivatives of Eisenstein series and height pairings, preprint, 1996.
  • [17] S. Kudla and J. Millson, The theta correspondence and harmonic forms I, Math. Ann. 274 (1986), no. 3, 353–378.
  • [18] S. Kudla and J. Millson, The theta correspondence and harmonic forms II, Math. Ann. 277 (1987), no. 2, 267–314.
  • [19] S. Kudla and J. Millson, Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, Inst. Hautes Études Sci. Publ. Math. (1990), no. 71, 121–172.
  • [20] S. Kudla and S. Rallis, On the Weil-Siegel formula, J. Reine Angew. Math. 387 (1988), 1–68.
  • [21] S. Kudla and S. Rallis, A regularized Siegel-Weil formula: the first term identity, Ann. of Math. (2) 140 (1994), no. 1, 1–80.
  • [22] S. Kudla and M. Rapoport, Cycles on Siegel $3$-folds and derivatives of Eisenstein series, preprint, 1996.
  • [23] J. S. Milne, Canonical models of (mixed) Shimura varieties and automorphic vector bundles, Automorphic Forms, Shimura Varieties and $L$-functions, Vol. I (Ann Arbor, MI, 1988) eds. L. Clozel and J. S. Milne, Perspect. Math., vol. 10, Academic Press, Boston, 1990, pp. 283–414.
  • [24] O. T. O'Meara, Introduction to Quadratic Forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117, Springer-Verlag, New York, 1963.
  • [25] R. Parthasarathy, Holomorphic forms in $\Gamma \backslash G/K$ and Chern classes, Topology 21 (1982), no. 2, 157–178.
  • [26] D. Prasad, Trilinear forms for representations of $\rm GL(2)$ and local $\epsilon$-factors, Compositio Math. 75 (1990), no. 1, 1–46.
  • [27] J. Rogawski, Automorphic representations of unitary groups in three variables, Ann. of Math. Stud., vol. 123, Princeton University Press, Princeton, 1990.
  • [28] I. Satake, Algebraic Structures of Symmetric Domains, Publ. Math. Soc. Japan, vol. 14, Princeton Univ. Press, Princeton, 1980.
  • [29] K.-Y. Shih, Existence of certain canonical models, Duke Math. J. 45 (1978), no. 1, 63–66.
  • [30] W. J. Sweet, The metaplectic case of the Weil-Siegel formula, thesis, Univ. of Maryland, 1990.
  • [31] A. Weil, Sur la théorie des formes quadratiques (1962), Collected Papers, Vol. II, Springer-Verlag, Berlin, 1979, pp. 471–484.
  • [32] R. O. Wells, Differential analysis on complex manifolds, Prentice-Hall Inc., Englewood Cliffs, N.J., 1973, Grad. Texts in Math. 65.