Algebraic cycles on Shimura varieties of orthogonal type

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Algebraic cycles on Shimura varieties of orthogonal type

Stephen S. Kudla

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

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Primary Subjects: 11F32

Secondary Subjects: 11F30, 11G18, 14C25, 14G35

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077242496
Mathematical Reviews number (MathSciNet): MR1427845
Zentralblatt MATH identifier: 0879.11026
Digital Object Identifier: doi:10.1215/S0012-7094-97-08602-6

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References

[1] Avner Ash, Nonminimal modular symbols for $\rm GL(n)$, Invent. Math. 91 (1988), no. 3, 483–491.

Mathematical Reviews (MathSciNet): MR89c:11089

Zentralblatt MATH: 0671.22005

Digital Object Identifier: doi:10.1007/BF01388782

[2] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura, J. Reine Angew. Math. 430 (1992), 69–83.

Mathematical Reviews (MathSciNet): MR93i:14017

Zentralblatt MATH: 0787.14011

Digital Object Identifier: doi:10.1515/crll.1992.430.69

[3] L. Clozel, Produits dans la cohomologie holomorphe des variétés de Shimura. II. Calculs et applications, J. Reine Angew. Math. 444 (1993), 1–15.

Mathematical Reviews (MathSciNet): MR95b:22030

Zentralblatt MATH: 0781.14014

Digital Object Identifier: doi:10.1515/crll.1993.444.1

[4] L. Clozel and T. N. Venkataramana, Restriction of holomorphic cohomology of a Shimura variety to a smaller Shimura variety, preprint, 1996.

Mathematical Reviews (MathSciNet): MR1646542

Zentralblatt MATH: 1037.11504

Digital Object Identifier: doi:10.1215/S0012-7094-98-09502-3

Project Euclid: euclid.dmj/1077229504

[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.

Mathematical Reviews (MathSciNet): MR95a:11047

Zentralblatt MATH: 0789.11033

Digital Object Identifier: doi:10.1007/BF02764643

[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.

Mathematical Reviews (MathSciNet): MR94m:11064

Zentralblatt MATH: 0807.11028

[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.

Mathematical Reviews (MathSciNet): MR94h:11046

Zentralblatt MATH: 0811.11026

Digital Object Identifier: doi:10.1007/BF01232433

[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.

Mathematical Reviews (MathSciNet): MR93g:11047

Zentralblatt MATH: 0807.11027

[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.

Mathematical Reviews (MathSciNet): MR85e:11037

Zentralblatt MATH: 0517.12008

[11] G. Harder, R. P. Langlands, and M. Rapoport, Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366 (1986), 53–120.

Mathematical Reviews (MathSciNet): MR87k:11066

Zentralblatt MATH: 0575.14004

[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.

Mathematical Reviews (MathSciNet): MR93a:11043

Zentralblatt MATH: 0731.11031

Digital Object Identifier: doi:10.2307/2944321

JSTOR: links.jstor.org

[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.

Mathematical Reviews (MathSciNet): MR56:11909

Zentralblatt MATH: 0332.14009

Digital Object Identifier: doi:10.1007/BF01390005

[14] M. Kneser, Darstellungsmasse indefiniter quadratischer Formen, Math. Z. 77 (1961), 188–194.

Mathematical Reviews (MathSciNet): MR25:3907

Zentralblatt MATH: 0100.03601

Digital Object Identifier: doi:10.1007/BF01180172

[15] S. Kudla, Intersection numbers for quotients of the complex $2$-ball and Hilbert modular forms, Invent. Math. 47 (1978), no. 2, 189–208.

Mathematical Reviews (MathSciNet): MR80a:10044

Zentralblatt MATH: 0399.10030

Digital Object Identifier: doi:10.1007/BF01578071

[16] S. Kudla, Central derivatives of Eisenstein series and height pairings, preprint, 1996.

Mathematical Reviews (MathSciNet): MR1491448

Zentralblatt MATH: 0990.11032

Digital Object Identifier: doi:10.2307/2952456

JSTOR: links.jstor.org

[17] S. Kudla and J. Millson, The theta correspondence and harmonic forms I, Math. Ann. 274 (1986), no. 3, 353–378.

Mathematical Reviews (MathSciNet): MR88b:11023

Zentralblatt MATH: 0594.10020

Digital Object Identifier: doi:10.1007/BF01457221

[18] S. Kudla and J. Millson, The theta correspondence and harmonic forms II, Math. Ann. 277 (1987), no. 2, 267–314.

Mathematical Reviews (MathSciNet): MR89b:11041

Zentralblatt MATH: 0618.10022

Digital Object Identifier: doi:10.1007/BF01457364

[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.

Mathematical Reviews (MathSciNet): MR92e:11035

Zentralblatt MATH: 0722.11026

Digital Object Identifier: doi:10.1007/BF02699880

[20] S. Kudla and S. Rallis, On the Weil-Siegel formula, J. Reine Angew. Math. 387 (1988), 1–68.

Mathematical Reviews (MathSciNet): MR90e:11059

Zentralblatt MATH: 0644.10021

[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.

Mathematical Reviews (MathSciNet): MR95f:11036

Zentralblatt MATH: 0818.11024

Digital Object Identifier: doi:10.2307/2118540

[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.

Mathematical Reviews (MathSciNet): MR91a:11027

Zentralblatt MATH: 0704.14016

[24] O. T. O'Meara, Introduction to Quadratic Forms, Die Grundlehren der mathematischen Wissenschaften, Bd. 117, Springer-Verlag, New York, 1963.

Mathematical Reviews (MathSciNet): MR27:2485

Zentralblatt MATH: 0107.03301

[25] R. Parthasarathy, Holomorphic forms in $\Gamma \backslash G/K$ and Chern classes, Topology 21 (1982), no. 2, 157–178.

Mathematical Reviews (MathSciNet): MR83b:32029

Zentralblatt MATH: 0484.57026

Digital Object Identifier: doi:10.1016/0040-9383(82)90003-9

[26] D. Prasad, Trilinear forms for representations of $\rm GL(2)$ and local $\epsilon$-factors, Compositio Math. 75 (1990), no. 1, 1–46.

Mathematical Reviews (MathSciNet): MR91i:22023

Zentralblatt MATH: 0731.22013

[27] J. Rogawski, Automorphic representations of unitary groups in three variables, Ann. of Math. Stud., vol. 123, Princeton University Press, Princeton, 1990.

Mathematical Reviews (MathSciNet): MR91k:22037

Zentralblatt MATH: 0724.11031

[28] I. Satake, Algebraic Structures of Symmetric Domains, Publ. Math. Soc. Japan, vol. 14, Princeton Univ. Press, Princeton, 1980.

Mathematical Reviews (MathSciNet): MR82i:32003

Zentralblatt MATH: 0483.32017

[29] K.-Y. Shih, Existence of certain canonical models, Duke Math. J. 45 (1978), no. 1, 63–66.

Mathematical Reviews (MathSciNet): MR81d:10020

Zentralblatt MATH: 0386.20023

Digital Object Identifier: doi:10.1215/S0012-7094-78-04505-2

Project Euclid: euclid.dmj/1077312687

[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.

Mathematical Reviews (MathSciNet): MR190097

[32] R. O. Wells, Differential analysis on complex manifolds, Prentice-Hall Inc., Englewood Cliffs, N.J., 1973, Grad. Texts in Math. 65.

Mathematical Reviews (MathSciNet): MR58:24309a

Zentralblatt MATH: 0262.32005

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