Cycles on Siegel threefolds and derivatives of Eisenstein series
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 5, pp. 695-756.
@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},
     pages = {695--756},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {5},
     year = {2000},
     doi = {10.1016/s0012-9593(00)01051-x},
     mrnumber = {2002e:11076b},
     zbl = {01571177},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)01051-x/}
}
TY  - JOUR
AU  - Kudla, Stephen S.
AU  - Rapoport, Michael
TI  - Cycles on Siegel threefolds and derivatives of Eisenstein series
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2000
SP  - 695
EP  - 756
VL  - 33
IS  - 5
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(00)01051-x/
DO  - 10.1016/s0012-9593(00)01051-x
LA  - en
ID  - ASENS_2000_4_33_5_695_0
ER  - 
%0 Journal Article
%A Kudla, Stephen S.
%A Rapoport, Michael
%T Cycles on Siegel threefolds and derivatives of Eisenstein series
%J Annales scientifiques de l'École Normale Supérieure
%D 2000
%P 695-756
%V 33
%N 5
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/s0012-9593(00)01051-x/
%R 10.1016/s0012-9593(00)01051-x
%G en
%F 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, Série 4, Tome 33 (2000) no. 5, pp. 695-756. doi : 10.1016/s0012-9593(00)01051-x. http://archive.numdam.org/articles/10.1016/s0012-9593(00)01051-x/

[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 | Zbl

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

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

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

[5] Fulton W., Intersection Theory, Springer-Verlag, Berlin, 1984. | MR | Zbl

[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. | EuDML | MR | Zbl

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

[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 | Zbl

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

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

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

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

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

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

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

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

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

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

[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 | Zbl

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

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

[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

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

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

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

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

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

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

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

[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 | Zbl

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

Cité par Sources :