Torsors and Rational Points [Hardcover]

This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.The subject of this book belongs to the 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.The subject of this book belongs to the 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.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.1. Introduction; 2. Torsors: general theory; 3. Examples of torsors; 4. Abelian torsors; 5. Obstructions over number fields; 6. Abelian descent and Manin obl<