Galois descent and cohomology for algebraic groups.
Ganzalgebraische Punkte und der Hilbertsche Irreduzibilitätssatz.
Gauss Sums and Elliptic Functions. I. The Kummer Sum.
General Selmer groups and critical values of Hecke L-functions.
Generalised Hermite constants, Voronoi theory and heights on flag varieties
This paper explores the study of the general Hermite constant associated with the general linear group and its irreducible representations, as defined by T. Watanabe. To that end, a height, which naturally applies to flag varieties, is built and notions of perfection and eutaxy characterising extremality are introduced. Finally we acquaint some relations (e.g., with Korkine–Zolotareff reduction), upper bounds and computation relative to these constants.
Generators and integer points on the elliptic curve y² = x³ - nx
Let E be an elliptic curve over the rationals ℚ given by y² = x³ - nx with a positive integer n. We consider first the case where n = N² for a square-free integer N. Then we show that if the Mordell-Weil group E(ℚ ) has rank one, there exist at most 17 integer points on E. Moreover, we show that for some parameterized N a certain point P can be in a system of generators for E(ℚ ), and we determine the integer points in the group generated by the point P and the torsion points. Secondly, we consider...
Geometrical model theory.
Géométrie, points entiers et courbes entières
Soit une variété projective sur un corps de nombres (resp. sur ). Soit la somme de « suffisamment de diviseurs positifs » sur . On montre que tout ensemble de points quasi-entiers (resp. toute courbe entière) dans est non Zariski-dense.
Global function fields with many rational places over the quinary field. II
Groupe de Selmer d'une courbe elliptique à multiplication complexe
Groupes de Galois attachés au points d'ordre fini des courbes elliptiques sur un corps de nombres (d'aprés J.P. Serre)