Nevanlinna-Cartan theory over function fields and a Diophantine equation.
Non-trivial in the Jacobian of an infinite family of curves of genus 2
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.
Notes on étale cohomology of number fields
Obstructions au principe de Hasse et à l’approximation faible
Si un système d’équations polynomiales à coefficients entiers admet une solution dans , il en admet sur tout complété -adique ou réel de . La réciproque a été démontrée par Hasse pour les quadriques, mais elle est fausse en général. Une grande partie des contre-exemples connus peuvent être expliqués à l’aide de l’obstruction de Brauer-Manin, basée sur la théorie du corps de classe. Il est donc naturel de se demander si, pour certaines classes de variétés, cette obstruction est la seule. Le but...
On algebraic tori of norm type.
On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
On diagonal cubic surfaces.
On galois automorphisms of the fundamental group of the projective line minus three points.
On K1 of curves over global fields.
On Manin's conditional algorithm
On Manin's conjecture for a certain singular cubic surface
On nonary cubic forms.
On -adic analytic families of Galois representations
On rational torsion points of central -curves
Let be a central -curve over a polyquadratic field . In this article we give an upper bound for prime divisors of the order of the -rational torsion subgroup (see Theorems 1.1 and 1.2). The notion of central -curves is a generalization of that of elliptic curves over . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].
On square values of quadratics
On squares of squares II
On the arithmetic of an elliptic curve over a -extension
On the Arithmetic of Special Values of L Functions.
On the behavior of Igusa,'s local zeta function in towers of field extension
On the Conjecture of Birch and Swinnerton-Dyer