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Displaying 121 – 132 of 132

The Hirzebruch-Mumford volume for the orthogonal group and applications.

Gritsenko, V., Hulek, K., Sankaran, G.K. (2007)

Documenta Mathematica

The modified diagonal cycle on the triple product of a pointed curve

Benedict H. Gross, Chad Schoen (1995)

Annales de l'institut Fourier

Let $X$ be a curve over a field $k$ with a rational point $e$ . We define a canonical cycle $Δ_{e} \in Z^{2} (X^{3})_{hom}$ . Suppose that $k$ is a number field and that $X$ has semi-stable reduction over the integers of $k$ with fiber components non-singular. We construct a regular model of $X^{3}$ and show that the height pairing $⟨ τ_{*} (Δ_{e}), τ_{*}^{'} (Δ_{e}) ⟩$ is well defined where $τ$ and $τ^{'}$ are correspondences. The paper ends with a brief discussion of heights and $L$ -functions in the case that $X$ is a modular curve.

The Picard group of Siegel modular threefolds.

R. Weissauer (1992)

Journal für die reine und angewandte Mathematik

Torsion points on elliptic curves and q-coeffincients of modular forms.

S. Kamienny (1992)

Inventiones mathematicae

Torsion points on the modular jacobian $J_{0} (N)$

Dino J. Lorenzini (1995)

Compositio Mathematica

Travaux de Shimura

Pierre Deligne (1970/1971)

Séminaire Bourbaki

Un exemple de feuilletage modulaire déduit d’une solution algébrique de l’équation de Painlevé VI

Gaël Cousin (2014)

Annales de l’institut Fourier

On peut construire facilement des exemples de connexions plates de rang $2$ sur $ℙ^{2}$ comme tirés en arrière de connexions sur $ℙ^{1}$ . On donne un exemple de connexion qui ne peut être obtenue de cette manière. Cet exemple est construit à partir d’une solution algébrique de l’équation de Painlevé VI. On en déduit un feuilletage modulaire. La preuve de ce fait repose sur la classification des feuilletages sur les surfaces projectives par leurs dimensions de Kodaira, fruit du travail de Brunella, McQuillan et...

Uniformisation $p$ -adique des variétés de Shimura

Jean-François Boutot (1996/1997)

Séminaire Bourbaki

Uniformization of certain Shimura curves

Pilar Bayer (2002)

Banach Center Publications

We present an approach to the uniformization of certain Shimura curves by means of automorphic functions, obtained by integration of non-linear differential equations. The method takes as its starting point a differential construction of the modular j-function, first worked out by R. Dedekind in 1877, and makes use of a differential operator of the third order, introduced by H. A. Schwarz in 1873.