Number Theory and Algebraic Geometry
by Miles Reid
ISBN No. 9780521545181
No.of pages 306
Sir Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume provides contemporary insight into several subjects in which Sir Peter's influence has been notable, and is dedicated to his 75th birthday. The opening section reviews some of his many remarkable contributions to mathematics and other fields. The remaining contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. The topics treated include: rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties.
Table of contents1. In lieu of birthday greetings J. B. Birch, Jean-Louis Colliot-Thelene, G. K. Sankaran, Miles Reid and Alexei Skorobogatov; 2. Peter Swinnerton-Dyer's mathematical papers to date; 3. On the Hasse principle for bielliptic surfaces Carmen Laura Basile and Alexei Skorobogatov; 4. Effective Diophantine approximation on Gm Enrico Bombieri and Paula B. Cohen; 5. A Diophantine system Andrew Bremner; 6. Valeurs d'un polynome ... une variable representees par une norme J.-L. Colliot-Thelene, D. Harari and A. N. Skorobogatov; 7. Constructing elements in Shafarevich-Tate groups of modular motives Neil Dummigan, William Stein and Mark Watkins; 8. A counterexample to a conjecture of Selmer Tom Fisher; 9. Linear relations amongst sums of two squares D. R. Heath-Brown; 10. Kronecker double series and the dilogarithm Andrey Levin; 11. On Shafarevich-Tate groups and the arithmetic of Fermat curves William G. McCallum and Pavlos Tzermias; 12. Cascades of projections from the log del Pezzo surfaces Miles Reid and Kaori Suzuki; 13. On obstructions to the Hasse principle Per Salberger; 14. Abelian surfaces with odd bilevel structure G. K. Sankaran.
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