Number Theory and Algebraic Geometry

This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Miles Reid (Edited by), Alexei Skorobogatov (Edited by)

9780521545181, Cambridge University Press

Paperback, published 26 January 2004

308 pages
22.4 x 15 x 1.5 cm, 0.417 kg

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.

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.

Subject Areas: Algebraic geometry [PBMW], Number theory [PBH]