Cycles on Siegel threefolds and derivatives of Eisenstein series
Kudla, Stephen S. ; Rapoport, Michael
Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000), p. 695-756 / Harvested from Numdam
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@article{ASENS_2000_4_33_5_695_0,
     author = {Kudla, Stephen S. and Rapoport, Michael},
     title = {Cycles on Siegel threefolds and derivatives of Eisenstein series},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {33},
     year = {2000},
     pages = {695-756},
     doi = {10.1016/s0012-9593(00)01051-x},
     mrnumber = {2002e:11076b},
     zbl = {01571177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2000_4_33_5_695_0}
}

Kudla, Stephen S.; Rapoport, Michael. Cycles on Siegel threefolds and derivatives of Eisenstein series. Annales scientifiques de l'École Normale Supérieure, Tome 33 (2000) pp. 695-756. doi : 10.1016/s0012-9593(00)01051-x. http://gdmltest.u-ga.fr/item/ASENS_2000_4_33_5_695_0/

[1] Boutot J.-F., Carayol H., Uniformisation p-adique des courbes de Shimura : les théorèmes de Cerednik et de Drinfeld, in : Courbes Modulaires et Courbes de Shimura, Astérisque, Vol. 196-197, 1991, pp. 45-158. | MR 1141456 | MR 93c:11041 | Zbl 0781.14010

[2] Deligne P., Travaux de Shimura, Sem. Bourbaki 389, Lecture Notes in Math., Vol. 244, Springer-Verlag, Berlin, 1971. | Numdam | MR 498581 | MR 58 #16675 | Zbl 0225.14007

[3] Deligne P., La conjecture de Weil pour les surfaces K3, Invent. Math. 15 (1972) 206-226. | MR 296076 | MR 45 #5137 | Zbl 0219.14022

[4] Eichler M., Quadratische Formen und orthogonale Gruppen, Springer-Verlag, Berlin, 1974. | MR 351996 | MR 50 #4484 | Zbl 0277.10017

[5] Fulton W., Intersection Theory, Springer-Verlag, Berlin, 1984. | MR 732620 | MR 85k:14004 | Zbl 0541.14005

[6] Genestier A., Letter to M. Rapoport, August 12, 1996.

[7] Gross B.H., Keating K., On the intersection of modular correspondances, Invent. Math. 112 (1993) 225-245. | MR 1213101 | MR 94h:11046 | Zbl 0811.11026

[8] Hashimoto K., Class numbers of positive definite ternary quaternion hermitian forms, Proc. Japan Acad. 59 (1983) 490-493. | MR 732595 | MR 85h:11019 | Zbl 0539.10020

[9] Hashimoto K., Ibukiyama T., On class numbers of positive definite binary quaternion hermitian forms, J. Fac. Sci. Univ. Tokyo, Sect IA 27 (1980) 549-601. | MR 603952 | MR 82j:10038 | Zbl 0452.10029

[10] Ibukiyama T., Katsura T., Oort F., Supersingular curves of genus two and class numbers, Compos. Math. 57 (1986) 127-152. | Numdam | MR 87f:14026 | Zbl 0589.14028

[11] Kaiser C., Ein getwistetes fundamentales Lemma für die GSp4, Bonner Mathematische Schriften 303 (1997). | MR 99k:11078 | Zbl 0899.11025

[12] Katsura T., Oort F., Families of supersingular abelian surfaces, Compos. Math. 62 (1987) 107-167. | Numdam | MR 88j:14053 | Zbl 0636.14017

[13] Kitaoka Y., A note on local representation densities of quadratic forms, Nagoya Math. J. 92 (1983) 145-152. | MR 85e:11029 | Zbl 0523.10012

[14] Kitaoka Y., Fourier coefficients of Eisenstein series of degree 3, Proc. Japan Acad. 60 (1984) 259-261. | MR 86d:11041 | Zbl 0551.10024

[15] Kitaoka Y., Arithmetic of Quadratic Forms, Cambridge Tracts in Mathematics, Vol. 106, Cambridge Univ. Press, Cambridge, UK, 1993. | MR 95c:11044 | Zbl 0785.11021

[16] Kottwitz R., Tamagawa numbers, Ann. Math. 127 (1988) 629-646. | MR 90e:11075 | Zbl 0678.22012

[17] Kottwitz R., Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (1992) 373-444. | MR 93a:11053 | Zbl 0796.14014

[18] Kudla S., Algebraic cycles on Shimura varieties of orthogonal type, Duke Math. J. 86 (1997) 39-78. | MR 98e:11058 | Zbl 0879.11026

[19] Kudla S., Central derivatives of Eisenstein series and height pairings, Ann. Math. 146 (1997) 545-646. | MR 99j:11047 | Zbl 0990.11032

[20] Kudla S., Millson J., Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, Publ. Math. Inst. Hautes Études Sci. 71 (1990) 121-172. | Numdam | MR 92e:11035 | Zbl 0722.11026

[21] Kudla S., Rapoport M., Arithmetic Hirzebruch Zagier cycles, J. Reine Angew. Math. 515 (1999) 155-244. | MR 2002e:11076a | Zbl 1048.11048

[22] Kudla S., Rapoport M., Height pairings on Shimura curves and p-adic uniformization, Invent. Math. (to appear). | Zbl 1009.11043

[23] Moret-Bailly L., Familles de courbes et de variétés abéliennes sur ℙ¹, II. exemple, in : Szpiro L. (Ed.), Séminaire sur les Pinceaux de Courbes de Genre au Moins Deux, Astérisque, Vol. 86, 1981, pp. 125-140. | Zbl 0515.14007

[24] Oort F., Which abelian surfaces are products of elliptic curves ?, Math. Ann. 214 (1975) 35-47. | MR 51 #519 | Zbl 0283.14007

[25] Ribet K., On modular representations of Gal(ℚ/ℚ) arising from modular forms, Invent. Math. 100 (1990) 431-476. | MR 91g:11066 | Zbl 0773.11039

[26] Ribet K., Bimodules and abelian surfaces, Adv. Stud. in Pure Math. 17 (1989) 359-407. | MR 92a:11070 | Zbl 0742.11033

[27] Serre J.-P., Algèbre Locale. Multiplicités, Lect. Notes in Math., Vol. 11, Springer-Verlag, Berlin, 1965. | MR 34 #1352 | Zbl 0142.28603

[28] Shih K.-Y., Existence of certain canonical models, Duke Math. J. 45 (1978) 63-66. | MR 81d:10020 | Zbl 0386.20023

[29] Shimura G., Arithmetic of alternating forms and quaternion hermitian forms, J. Math. Soc. Japan 15 (1963) 63-65. | MR 26 #3694 | Zbl 0121.28102

[30] Stamm H., On the reduction of the Hilbert-Blumenthal moduli scheme with Г0(p)-level structure, Forum Math. 9 (1997) 405-455. | MR 98h:14030 | Zbl 0916.14022

[31] Sweet W.J., A computation of the gamma matrix of a family of p-adic zeta integrals, J. Number Theory 55 (1995) 222-260. | MR 96m:11108 | Zbl 0862.14015

[32] Tonghai Yang, An explicit formula for local densities of quadratic forms, J. Number Theory 72 (1998) 309-356. | MR 99j:11034 | Zbl 0930.11021