Sur la formule de Deuring-Safarevic et un résultat de Nakajima.
Sur la mauvaise réduction des courbes de Shimura
Sur la recherche des -extensions non ramifiées de
Sur le corps de définition de certaines courbes elliptiques à multiplications complexes.
Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive.
Sur les -structures attachées aux courbes de Mumford
Sur les transformations polynômiales et rationnelles
Terms in elliptic divisibility sequences divisible by their indices
Tetragonal modular curves
The absolute anabelian geometry of canonical curves.
The arithmetic of curves defined by iteration
We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...
The arithmetic of Fermat curves.
The Brauer–Manin obstruction for curves having split Jacobians
Let be a non-constant morphism from a curve to an abelian variety , all defined over a number field . Suppose that is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that and are finite.
The canonical height and integral points on elliptic curves.
The class group of a one-dimensional affinoid space
A curve over a non-archimedean valued field is with respect to its analytic structure a finite union of affinoid spaces. The main result states that the class group of a one dimensional, connected, regular affinoid space is trivial if and only if is a subspace of . As a consequence, has locally a trivial class group if and only if the stable reduction of has only rational components.
The cuspidal torsion packet on hyperelliptic Fermat quotients
Let be a prime, be the non-singular projective curve defined over by the affine model , the point of at infinity on this model, the Jacobian of , and the albanese embedding with as base point. Let be an algebraic closure of . Taking care of a case not covered in [12], we show that consists only of the image under of the Weierstrass points of and the points and , where denotes the torsion points of .
The Diophantine equation f(x) = g(y)
The genus of curves over finite fields with many rational points.
The Index of Stickelberger Ideals of Order2 and Cuspidal Class Numbers .
The intrinsic Hodge theory of -adic hyperbolic curves.