Symmetrische Modulflächen der Diskriminante p2.
Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere
We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system....
Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields.
Systèmes de Honda des schémas en -vectoriels
Tamagawa number of reductive algebraic groups
Tate duality and ramification of division algebras
Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication.
Terms in elliptic divisibility sequences divisible by their indices
Terne di quadrati consecutivi in un campo di Galois
Explicit formulae for the number of triplets of consecutive squares in a Galois field are given.
The absolute anabelian geometry of canonical curves.
The absolute Galois group of a pseudo real closed field
The algebraic groups leading to the Roth inequalities
We determine the algebraic groups which have a close relation to the Roth inequalities.
The Algebraic nature of the elementary theory of PRC fields.
The annihilation of divisor classes in abelian extensions of the rational function field
The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms
In this paper we extend the arithmetic Grothendieck-Riemann-Roch Theorem to projective morphisms between arithmetic varieties that are not necessarily smooth over the complex numbers. The main ingredient of this extension is the theory of generalized holomorphic analytic torsion classes previously developed by the authors.
The arithmetic of certain del Pezzo surfaces and K3 surfaces
We construct del Pezzo surfaces of degree violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.
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 Elliptic Curves.
The arithmetic of Fermat curves.
The arithmetic of function fields