Buch, Englisch, Band 144, 196 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 443 g
Buch, Englisch, Band 144, 196 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 443 g
Reihe: Cambridge Tracts in Mathematics
ISBN: 978-0-521-80237-6
Verlag: Cambridge University Press
The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book represents the first detailed exposition of 1) the general theory of torsors with key examples, 2) the relation of descent to the Manin obstruction, and 3) applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.
