The p-Rank of Artin-Schreier Curves.
The Prym variety for a cyclic unramified cover of a hyperelliptic Riemann surface.
The rank of hyperelliptic Jacobians in families of quadratic twists
The variation of the rank of elliptic curves over in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over admits infinitely many quadratic twists of rank . Most elliptic curves have even infinitely many twists of rank and examples of elliptic curves with infinitely many twists of rank are known. There are also certain density results. This paper studies the variation of the...
The rank-one limit of the Fourier-Mukai transform.
The Strong Lefschetz Principle in Algebraic Geometry.
The trisecant conjecture.
Théorèmes de Lefschetz pour les lieux de dégénérescence
Theta loci and deformation theory
We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.
Torelli theorem for stable curves
We study the Torelli morphism from the moduli space of stable curves to the moduli space of principally polarized stable semi-abelic pairs. We give two characterizations of its fibers, describe its injectivity locus, and give a sharp upper bound on the cardinality of finite fibers. We also bound the dimension of infinite fibers.
Torsion points on elliptic curves and q-coeffincients of modular forms.
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.
Torsion points on the modular jacobian
Torsion sur des familles de courbes de genre g.
Transcendance de valeurs de la fonction gamma
Translation manifolds and the converse of Abel's theorem
Two Extremal elliptic fibrations on Jacobian Kummer surfaces.