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[null,"1.","Record Nr.",null,"UNISA996466644903316"]
[null,null,"Autore",null,"Wittenberg Olivier"]
[null,null,"Titolo",null,"Intersections de deux quadriques et pinceaux de courbes de genre 1 [[electronic resource] ] : Intersections of two quadrics and pencils of curves of genus 1 / / by Olivier Wittenberg"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2007"]
[null,null,"ISBN",null,"3-540-69141-3"]
[null,null,"Edizione",null,"[1st ed. 2007.]"]
[null,null,"Descrizione fisica",null,"1 online resource (viii, 218 p.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 1901"]
[null,null,"Disciplina",null,"512.7"]
[null,null,"Soggetti",null,"Number theory"]
[{"$nulls":4},"Algebraic geometry"]
[{"$nulls":4},"Number Theory"]
[{"$nulls":4},"Algebraic Geometry"]
[null,null,"Lingua di pubblicazione",null,"Francese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"Arithmétique des pinceaux semi-stables de courbes de genre 1 (première partie) -- Arithmétique des pinceaux semi-stables de courbes de genre 1 (seconde partie) -- Principe de Hasse pour les surfaces de del Pezzo de degré 4."]
[null,null,null,"Sommario/riassunto","Cet ouvrage est consacré à l'arithmétique des surfaces fibrées en courbes de genre 1 au-dessus de la droite projective, et à l'arithmétique des intersections de deux quadriques dans l'espace projectif. Swinnerton-Dyer introduisit en 1993 une technique permettant d'étudier les points rationnels des pinceaux de courbes de genre 1. La première moitié de l'ouvrage reprend et développe cette technique ainsi que ses généralisations ultérieures. La seconde moitié, qui repose sur la première, porte sur les surfaces de del Pezzo de degré 4 et sur les intersections de deux quadriques de dimension supérieure; les résultats annoncés dans [C. R. Math. Acad. Sci. Paris 342 (2006), no. 4, 223--227] y sont démontrés. This research monograph focuses on the arithmetic, over number fields, of surfaces fibred into curves of genus 1 over the projective line, and of intersections of two quadrics in projective space. The first half contains a complete account of the technique initiated by Swinnerton-Dyer in 1993 for studying rational points on pencils of curves of genus 1, while incorporating and generalising most of its subsequent refinements. The second half, "]
[{"$nulls":4},"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]."]