Rational Points on Algebraic Varieties

Diagonal cubic equations in four variables with prime coefficients.- References.- Rational points on cubic surfaces.- 1. Notations and preliminaries.- 2. Ternary quadratic forms.- 3. Proof of the main theorem.- References.- Torseurs arithmetiques et espaces fibres.- Notations et conventions.- 1. Torseurs arithmetiques.- 2. Espaces fibres.- References.- Fonctions zeta des hauteurs des espaces fibres.- Notationset conventions.- 3. Fonctions holomorphes dans un tube.- 4. Varietes toriques.- 5. Application aux fibrations en varietes toriques.- Appendice A. Un theoreme tauberien.- Appendice B. Demonstration de quelques inegalites.- References.- Hasse principle for pencils of curves of genus one whose Jacobians have a rational 2-division point, close variation on a paper of Bender and Swinnerton-Dyer.- Statement of the Theorems.- 1. Selmer groups associated to a degree 2 isogeny.- 2. Proof of Theorem A.- 3. Proof of Theorem B.- References.- Enriques surfaces with a dense set of rational points, Appendix to the paper by J.-L. Colliot-Thelene.- References.- Density of integral points on algebraic varieties.- 1. Generalities.- 2. Geometry.- 3. The fibration method and nondegenerate multisections.- 4. Approximation techniques.- 5. Conic bundles and integral points.- 6. Potential density for log K3 surfaces.- References.- Composition of points and the Mordell-Weil problem for cubic surfaces.- 1. Introduction.- 2. Cardinality of generators of subgroups in a reflection group.- 3. Structure of universal equivalence.- 4. A group-theoretic description of universal equivalence.- 5. Birationally trivial cubic surfaces: a finiteness theorem.- References.- Torseurs universels et methode du cercle.- 1. Une version raffinee d'une conjecture de Manin.- 2. Passage au torseur universel.- 3. Intersections completes.- 4. Conclusion.- References.- Tamagawa numbers of diagonal cubic surfaces of higher rank.- 1. Description of the conjectural constant.- 2. The Galois module Pic($$bar{V}$$).- 3. Euler product for the good places.- 4. Density at the bad places.- 5. The constant a(V).- 6. Some statistical formulae.- 7. Presentation of the results.- References.- The Hasse principle for complete intersections in projective space.- References.- Une construction de courbes k-rationnelles sur les surfaces de Kummer d'un produit de courbes de genre 1..- 1. Relevement des courbes de P1,k x P1,k sur la surface de Kummer.- 2. Exemples.- References.- Arithmetic Stratifications and Partial Eisenstein Series.- 1. The fibre bundles: geometric-arithmetic preliminaries.- 2. Height zeta functions.- 3. Arithmetic stratification.- References.- Weak Approximation and R-equivalence on Cubic Surfaces.- 1. Introduction.- 2. Geometric background.- 3. Approximation at an infinite prime.- 4. Approximation at a finite prime.- 5. The lifting process.- 6. The dense lifting process.- 7. Adelic results.- 8. Surfaces X13 + X23 + X33 ? dX03 = 0.- References.- Hua's lemma and exponential sums over binary forms.- 1. Introduction.- 2. Preliminary reductions.- 3. Integral points on affine plane curves.- 4. The inductive step.- 5. The completion of the proof of Theorem 1.1.- References.