Points de petite hauteur sur les courbes modulaires X0(N)

被引：2

作者：

Michel P. ^{[1
]}

Ullmo E. ^{[1
]}

机构：

[1] Universite Paris-Sud, Mathematiques, Bâtiment 425

来源：

Inventiones mathematicae | 1998年 / 131卷 / 3期

关键词：

Explicit Form; Trace Formula; Dualizing Sheaf; Modular Curf; Bogomolov Conjecture;

D O I：

10.1007/s002220050216

中图分类号：

学科分类号：

摘要：

Let N be a square free integer, prime to 6. Let φ the imbeding of X0(N) in its Jacobian relative to the point ∞. We show that the set {x ∈ X0(N)(Q̄) |hNT(φ(x)) ≤ (2/3 - ε) log N} is finite and that {x ∈ X0(N)(Q̄) |hNT((φ(x)) ≤ (4/3 + ε) logN} is infinite. This explicit form of the Bogomolov conjecture is obtained by an estimation of the self-intersection of the dualizing sheaf, in the sense of Arakelov theory, of modular curves. This result is obtained by estimating several quantities attached to the Arakelov metric on X0(N), starting with Petersson's trace formula.

引用

页码：645 / 674

页数：29

共 24 条

[1]

Abbes A., Ullmo E., Comparaison des métriques d'arakelov et de poincaré sur X<sub>0</sub>(N), Duke Mathematical Journal, 80, 2, pp. 295-307, (1995)

[2]

Abbes A., Ullmo E., Auto-intersection du dualisant relatif des courbes modulaires X<sub>0</sub>(N), à paraitre au, J. Reine Angew. Math.

[3]

Arakelov S.J., Intersection theory of divisors on an arithmetic surface, Math. USSR-Izv., 8, pp. 1167-1180, (1974)

[4]

Bost J.-B., Mestre J.-F., Moret-Bailly L., Sur le Calcul Explicite des "classes de Chern" des Surfaces Arithmétiques de Genre 2, dans Séminaire sur les Pinceaux de Courbes Elliptiques (à la Recherche de "Mordell Effectif"), 183, pp. 69-105, (1990)

[5]

Coates B.J., Schmidt W., Iwasawa theory for the symmetric square of an elliptic curve, J. Reine Angew. Math., pp. 57-60, (1987)

[6]

Deligne P., Rapoport M., Schémas de modules des courbes elliptiques, dans modular functions of one variable II, Lectures Notes in Mathematics, 349, (1973)

[7]

Deshouillers J.M., Iwaniec H., Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math, 70, pp. 219-288, (1982)

[8]

Duke W., Friedlander J.B., Iwaniec H., Bounds for autornorphic L-functions II, Invent. Math, 115, pp. 219-239, (1994)

[9]

Duke W., On the dimension of the space of forms of weight 1, Inter. Math. Res. Notices, 2, pp. 99-109, (1995)

[10]

Drinfeld V.G., Two Theorems on Modular Curves, Functional Analysis and Its Applications, 7, 2, pp. 155-156, (1973)

← 1 2 3 →