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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...

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