Intersections de deux quadriques et pinceaux de courbes de genre 1 / Olivier Wittenberg
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1901Langue : français.Éditeur : Berlin : Springer, 2007ISBN: 9783540691372.ISSN: 1617-9692.Sujet MSC : 11G35, Arithmetic algebraic geometry (Diophantine geometry), Varieties over global fields14J20, Algebraic geometry - Surfaces and higher-dimensional varieties, Arithmetic ground fields
14J27, Algebraic geometry - Surfaces and higher-dimensional varieties, Elliptic surfaces, elliptic or Calabi-Yau fibrations
14J26, Algebraic geometry - Surfaces and higher-dimensional varieties, Rational and ruled surfaces
11D25, Number theory - Diophantine equations, Cubic and quartic Diophantine equationsEn-ligne : Springerlink | Zentralblatt | MathSciNet
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The monograph under review grew out of the author’s Ph.D thesis. Its main objects, smooth intersections of two quadrics in a projective space defined over a number field (which include an important particular case of del Pezzo surfaces of degree 4), have been extensively studied during the past decades. The focus has been made on the Hasse principle (in particular, on the problem whether the Brauer-Manin obstruction to this principle to hold is the only one). The author proves two important general results. ... (Zentralblatt)
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