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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Commutative Group Schemes
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Beschreibung
We restrict ourselves to two aspects of the field of group schemes, in which the results are fairly complete: commutative algebraic group schemes over an algebraically closed field (of characteristic different from zero), and a duality theory concern ing abelian schemes over a locally noetherian prescheme. The prelim inaries for these considerations are brought together in chapter I. SERRE… described properties of the category of commutative quasi-algebraic groups by introducing pro-algebraic groups. In char8teristic zero the situation is clear. In characteristic different from zero information on finite group schemee is needed in order to handle group schemes; this information can be found in work of GABRIEL. In the second chapter these ideas of SERRE and GABRIEL are put together. Also extension groups of elementary group schemes are determined. A suggestion in a paper by MANIN gave crystallization to a fee11ng of symmetry concerning subgroups of abelian varieties. In the third chapter we prove that the dual of an abelian scheme and the linear dual of a finite subgroup scheme are related in a very natural way. Afterwards we became aware that a special case of this theorem was already known by CARTIER and BARSOTTI. Applications of this duality theorem are: the classical duality theorem ("duality hy pothesis", proved by CARTIER and by NISHI); calculation of Ext(~a,A), where A is an abelian variety (result conjectured by SERRE); a proof of the symmetry condition (due to MANIN) concerning the isogeny type of a formal group attached to an abelian variety. 26,74 €
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Technische Daten
Erscheinungsdatum
01.01.1966
Sprache
Englisch
EAN
9783540035985
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Lecture Notes in Mathematics
Sonderedition
Nein
Autor
F. Oort
Seitenanzahl
136
Einbandart
Broschiert
Schlagwörter
Abelian variety, Group, Kommutative Algebra, Mathematik, algebra
Thema-Inhalt
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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