The Arithmetic Theory of Local Constants for abelian Varieties
The Cassels-Tate pairing on polarized Abelian varieties.
The conductor of an abelian variety
The Eisenstein descent on J0 (N).
The groups of points on abelian varieties over finite fields
Let A be an abelian variety with commutative endomorphism algebra over a finite field k. The k-isogeny class of A is uniquely determined by a Weil polynomial f A without multiple roots. We give a classification of the groups of k-rational points on varieties from this class in terms of Newton polygons of f A(1 − t).
The Mordell conjecture revisited
The -rank stratification of Artin-Schreier curves
We study a moduli space for Artin-Schreier curves of genus over an algebraically closed field of characteristic . We study the stratification of by -rank into strata of Artin-Schreier curves of genus with -rank exactly . We enumerate the irreducible components of and find their dimensions. As an application, when , we prove that every irreducible component of the moduli space of hyperelliptic -curves with genus and -rank has dimension . We also determine all pairs for...
The polynomial and elliptic curves of conductor 11
The structure of Gauss-like maps
The tame fundamental group of an abelian variety and integral points
The Tate conjecture for certain abelian varieties over finite fields
The Tate conjecture for ordinary K3 surfaces over finite fields.
The topology of rational points.
Théorie de Kummer sur les groupes algébriques
Théorie des modèles et conjecture de Manin-Mumford
Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
In recent papers we proved a special case of a variant of Pink’s Conjecture for a variety inside a semiabelian scheme: namely for any curve inside anything isogenous to a product of two elliptic schemes. Here we go beyond the elliptic situation by settling the crucial case of any simple abelian surface scheme defined over the field of algebraic numbers, thus confirming an earlier conjecture of Shou-Wu Zhang. This is of particular relevance in the topic, also in view of very recent counterexamples...
Torsion points on fermat curves
Torsion points on Jacobians of quotients of Fermat curves and p-adic soliton theory.
Twists of Modular Forms and Endomorphisms of Abelian Varieties.