F. Oort: Commutative Group Schemes

Cover: 9783540035985 | Commutative Group Schemes | F. Oort | Taschenbuch | Englisch

Rückseite: 9783540035985 | Commutative Group Schemes | F. Oort | Taschenbuch | Englisch

Dekorationsartikel gehören nicht zum Leistungsumfang.

Sprache: Englisch

26,20 €

inkl. MwSt.

Versandkostenfrei per Post / DHL

Lieferzeit 4-7 Werktage

Kategorien:

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.

Inhaltsverzeichnis

Preliminaries.- Algebraic group schemes.- Duality theorems for abelian schemes.

Details

Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	Einband - flex.(Paperback)
ISBN-13:	9783540035985
ISBN-10:	3540035982
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Oort, F.
Hersteller:	Springer Springer Spektrum Springer-Verlag GmbH Lecture Notes in Mathematics
Verantwortliche Person für die EU:	Springer Nature Customer Service Center GmbH, Europaplatz 3, D-69115 Heidelberg, productsafety@springernature.com
Maße:	235 x 155 x 9 mm
Von/Mit:	F. Oort
Gewicht:	0,23 kg