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TitleRational Points on Algebraic Varieties [electronic resource] / edited by Emmanuel Peyre, Yuri Tschinkel
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8368-9
Descript XVI, 446 p. online resource

CONTENT

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 arithmรฉtiques et espaces fibrรฉs -- Notations et conventions -- 1. Torseurs arithmรฉtiques -- 2. Espaces fibrรฉs -- Rรฉfรฉrences -- Fonctions zรชta des hauteurs des espaces fibrรฉs -- Notationset conventions -- 3. Fonctions holomorphes dans un tube -- 4. Variรฉtรฉs toriques -- 5. Application aux fibrations en variรฉtรฉs toriques -- Appendice A. Un thรฉorรจme taubรฉrien -- Appendice B. Dรฉmonstration de quelques inรฉgalitรฉs -- Rรฉfรฉrences -- 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-Thรฉlรจne -- 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 Mordellโ{128}{147}Weil problem for cubic surfaces -- 1. Introduction -- 2. Cardinality of generators of subgroups in a reflection group -- 3. Structure of universal equivalence -- 4. A groupโ{128}{147}theoretic description of universal equivalence -- 5. Birationally trivial cubic surfaces: a finiteness theorem -- References -- Torseurs universels et mรฉthode du cercle -- 1. Une version raffinรฉe dโ{128}{153}une conjecture de Manin -- 2. Passage au torseur universel -- 3. Intersections complรจtes -- 4. Conclusion -- Rรฉfรฉrences -- 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 dโ{128}{153}un produit de courbes de genre 1. -- 1. Relรจvement des courbes de P1,k ร{151} P1,k sur la surface de Kummer -- 2. Exemples -- Rรฉfรฉrences -- 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 -- Huaโ{128}{153}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


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