Let G be a linear algebraic group and X be an irreducible algebraic variety with a generically free G-action, all defined over an algebraically closed base field of characteristic zero. It is well known that X can be viewed as a G-torsor, representing a class [X] in H 1 (K, G), where K is the field
β¦ LIBER β¦
Torsors and rational points
β Scribed by Alexei Skorobogatov
- Book ID
- 127417940
- Publisher
- Cambridge University Press
- Year
- 2001
- Tongue
- English
- Weight
- 2 MB
- Series
- Cambridge tracts in mathematics 144
- Category
- Library
- City
- Cambridge; New York
- ISBN-13
- 9780521802376
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
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