A homological criterion for reducibility of analytic spaces, with application to characterizing the theta divisor of a product of two general principally polarized abelian varieties.
A Kummer criterion for imaginary quadratic fields
A Lefschetz decomposition for Chow motives of abelian schemes.
A local-global principle for rational isogenies of prime degree
Let be a number field. We consider a local-global principle for elliptic curves that admit (or do not admit) a rational isogeny of prime degree . For suitable (including ), we prove that this principle holds for all , and for , but find a counterexample when for an elliptic curve with -invariant . For we show that, up to isomorphism, this is the only counterexample.
A memoir on the double ...-functions.
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. I.
A New Compactification of the Siegel Space and Degeneration of Abelian Varieties. II.
A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
A note on a theorem of Griffiths on the Abel-Jacobi map.
A Note on height pairings on polarized abelian varieties
Let be an abelian variety defined over a number field . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.
A Note on Height Pairings, Tamagawa Numbers, and the Birch and Swinnerton-Dyer Conjecture.
A note on minimal Galois embeddings of abelian surfaces
A propos de l' espace des modules de fibrés de rang 2 sur une courbe.
A remark on the Picard group of spin moduli space
We describe a number of classes in the Picard group of spin moduli space and determine the relations they satisfy; as an application we show that the Picard group in question contains 4-torsion elements.
A result on the integral chow ring of a generic principally polarized complex abelian variety of dimension four
A Riemann-Hurwitz formula for the Selmer group of an elliptic curve with complex multiplication.
A series of smooth irregular varieties in projective space
A Siegel modular 3-fold that is a Picard modular 3-fold
A special case of the Garnier system, -polarized abelian surfaces and their moduli
A theorem of Gieseker-Petri type for Prym varieties