Number Theory and Algebraic Geometry
Number Theory and Algebraic Geometry
Miles Reid, University of Warwick
Alexei Skorobogatov, Imperial College of Science, Technology and Medicine, London
Alexei Skorobogatov, Imperial College of Science, Technology and Medicine, London
February 2004
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9780521545181
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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.
- Top-notch contributor list
- Lively overview of several exciting areas of analytic and algebraic number theory and algebraic geometry close to Sir Peter Swinnerton-Dyer's research interests
- Introduction is light-hearted description of Sir Peter Swinnerton-Dyer's remarkable mathematical career stretching over 60 years' work of amazing originality
Product details
February 2004Paperback
9780521545181
308 pages
224 × 150 × 15 mm
0.417kg
Available
Table of Contents
- 1. In lieu of birthday greetings J. B. Birch, Jean-Louis Colliot-Thélène, 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 polynôme à une variable representées par une norme J.-L. Colliot-Thélène, 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.
