Decomposition of non-archimedean analytic tori
Decompositions of an Abelian surface and quadratic forms
When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.
Deformations of theta divisors and the rank 4 quadrics problem
Degenerations of Prym varieties and intersections of three quadrics.
Degrees of curves in abelian varieties
Denominators of Igusa class polynomials
In [22], the authors proved an explicit formula for the arithmetic intersection number on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field . These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 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...
Der Definitionskörper für den Zerfall einer abelschen Varietät mit komplexer Multiplikation.
Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen.
Derived invariance of the number of holomorphic -forms and vector fields
We prove that smooth projective varieties with equivalent derived categories have isogenous Picard varieties. In particular their irregularity and number of independent vector fields are the same. This implies that all Hodge numbers are the same for arbitrary derived equivalent threefolds, as well as other consequences of derived equivalence based on numerical criteria.
Descent via isogeny in dimension 2
Descente infinie et hauteur p-adique sur les courbes elliptiques à multiplication complexe.
Die Modulargleichungen der hyperelliptischen Functionen erster Ordnung für die Transformation fünften Grades
Die partiellen Differentialgleichungen der hyperelliptischen Thetafunctionen
Differential characters and characteristic polynomial of Frobenius.
Differential characters of abelian varieties over p-adic fields.
Dimensions of spaces of cusp forms over function fields.
Diophantine Approximation and Lattices with Complex Multiplication.
Diophantine Approximation on Abelian Varieties with Complex Mulitplication.
Distinguishing Prymians from Jacobians.