Torsors and Rational Points

ISBN-13: 9780521802376 / Angielski / Twarda / 2001 / 196 str.

Alexei Skorobogatov; A. Skorobogatov; B. Bollobas

Opis

The subject of this book is arithmetic algebraic geometry, an area between number theory and algebraic geometry. It is about applying geometric methods to the study of polynomial equations in rational numbers (Diophantine equations). This book represents the first complete and coherent exposition in a single volume, of both the theory and applications of torsors to rational points. Some very recent material is included. It is demonstrated that torsors provide a unified approach to several branches of the theory which were hitherto developing in parallel.

Recenzje

'The book is written in a clear and lucid manner with detailed examples that balance the abstract theory with concrete facts. It is reasonably self-contained and can therefore be recommended to newcomers to the recent development of the descent'. EMS

Spis treści

1. Introduction; 2. Torsors: general theory; 3. Examples of torsors; 4. Abelian torsors; 5. Obstructions over number fields; 6. Abelian descent and Manin obstruction; 7. Conic bundle surfaces; 8. Bielliptic surfaces; 9. Homogenous spaces.