Verwandte Artikel zu Commutative Group Schemes: 15 (Lecture Notes in Mathematics)
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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.
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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.
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Commutative Group Schemes
Verlag:
Springer Berlin Heidelberg, 1966
ISBN 10: 3540035982
ISBN 13: 9783540035985
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Commutative Group Schemes
Verlag:
Springer Berlin Heidelberg, 1966
ISBN 10: 3540035982
ISBN 13: 9783540035985
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Commutative group schemes. (= Lecture notes in mathematics, Band 15).
Verlag:
Springer Berlin, 1966
ISBN 10: 3540035982
ISBN 13: 9783540035985
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4°, Softcover/Paperback. 1.Auflage,. VIII, 125 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540035985 Sprache: Englisch Gewicht in Gramm: 650. Bestandsnummer des Verkäufers 154145
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Commutative group schemes. (= Lecture notes in mathematics, Band 15).
Verlag:
Springer Berlin, 1966
ISBN 10: 3540035982
ISBN 13: 9783540035985
Gebraucht
4°, Softcover/Paperback
Erstausgabe
Anbieter: Antiquariat Deinbacher, Murstetten, Österreich
Verkäuferbewertung 4 von 5 Sternen
4°, Softcover/Paperback. 1.Auflage,. VIII, 125 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540035985 Sprache: Englisch Gewicht in Gramm: 650. Bestandsnummer des Verkäufers 154219
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Transitive Erweiterungen endlicher Permutationsgruppen. (= Lecture notes in mathematics, Band 84).
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4°, Softcover/Paperback. 1.Auflage,. VIII, 119 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540035985 Sprache: Englisch Gewicht in Gramm: 650. Bestandsnummer des Verkäufers 154146
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Commutative Group Schemes
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Commutative Group Schemes
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Bestandsnummer des Verkäufers 9783540035985
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Commutative Group Schemes
ISBN 10: 3540035982
ISBN 13: 9783540035985
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Taschenbuch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 144 pp. Englisch. Bestandsnummer des Verkäufers 9783540035985
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Commutative Group Schemes
Verlag:
Springer Berlin Heidelberg Jan 1966, 1966
ISBN 10: 3540035982
ISBN 13: 9783540035985
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Anbieter: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Deutschland
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 144 pp. Englisch. Bestandsnummer des Verkäufers 9783540035985
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Commutative Group Schemes (Lecture Notes in Mathematics, 15)
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