| Description |
1 online resource (viii, 218 pages) |
| Series |
Lecture notes in mathematics, 0075-8434 ; 1901 |
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Lecture notes in mathematics (Springer-Verlag) ; 1901.
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| Contents |
Arithmétique des pinceaux semi-stables de courbes de genre 1 (première partie) -- Arithmétique des pinceaux semi-stables de courbes de genre 1 (seconde partie) -- Principe de Hasse pour les surfaces de del Pezzo de degré 4 |
| Summary |
Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'étudier les points rationnels des pinceaux de courbes de genre 1. La première moitié de l'ouvrage reprend et développe cette technique ainsi que ses généralisations ultérieures. La seconde moitié, qui repose sur la première, porte sur les surfaces de del Pezzo de degré 4 et sur les intersections de deux quadriques de dimension supérieure; les résultats annoncés dans [C.R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] y sont démontrés. This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half contains a complete account of the technique initiated by Swinnerton-Dyer in 1993 for studying rational points on pencils of curves of genus 1, while incorporating and generalising most of its subsequent refinements. The second half, which builds upon the first, is devoted to quartic del Pezzo surfaces and higher-dimensional intersections of two quadrics. It culminates in the proof of the results announced in [C.R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] |
| Bibliography |
Includes bibliographical references (pages 209-213) and index |
| Notes |
In French, supplemented with an introduction in English |
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Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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Print version record |
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digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| In |
Springer e-books |
| Subject |
Quartic surfaces.
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Quadrics.
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Matrix pencils.
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Geometry, Algebraic.
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MATHEMATICS -- Geometry -- Algebraic.
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Geometry, Algebraic.
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Quartic surfaces.
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Quadrics.
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Matrix pencils.
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Geometry, Algebraic
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Matrix pencils
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Quadrics
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Quartic surfaces
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Algebraïsche meetkunde.
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Diofantische analyse.
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Superfícies algébricas.
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Geometria algébrica.
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Geometry, Algebraic.
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Arithmetical algebraic geometry.
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| Form |
Electronic book
|
| ISBN |
9783540691419 |
|
3540691413 |
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3540691375 |
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9783540691372 |
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