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Denominators of Igusa class polynomials

Kristin Lauter, Bianca Viray (2014)

Publications mathématiques de Besançon

In [22], the authors proved an explicit formula for the arithmetic intersection number $(CM (K) . G_{1})$ on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field $K$ . These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus $2$ curves for use in cryptography. One of the main tools in the proof was a previous result of the authors [21] generalizing the singular moduli formula of Gross...

Derivatives of Eisenstein series and generating functions for arithmetic cycles

Stephen S. Kudla (1999/2000)

Séminaire Bourbaki

Descente infinie et hauteur p-adique sur les courbes elliptiques à multiplication complexe.

Bernadette Perrin-Riou (1982/1983)

Inventiones mathematicae

Direct images in non-archimedean Arakelov theory

Henri Gillet, Christophe Soulé (2000)

Annales de l'institut Fourier

We develop a formalism of direct images for metrized vector bundles in the context of the non-archimedean Arakelov theory introduced in our joint work with S. Bloch. We prove a Riemann-Roch-Grothendieck theorem for this direct image.

Distribution des points de petite hauteur dans les groupes multiplicatifs

Francesco Amoroso, Sinnou David (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove a new lower bound for the height of points on a subvariety $V$ of a multiplicative torus, which lie outside the union of torsion subvarieties of $V$ . Although lower bounds for the heights of these points where already known (decreasing multi-exponential function of the degree for Scmhidt and Bombieri–Zannier, [Sch], [Bo-Za], and inverse monomial in the degree by the second author of this note and P. Philippon, [Da-Phi]), our method provesup to an $ε$ the sharpest conjectures that can be formulated....