Models of Genus One Curves - Couverture souple

Sadek, Mohammad

 
9783843353847: Models of Genus One Curves
Couverture souple
ISBN 10 : 3843353840 ISBN 13 : 9783843353847
Editeur : LAP LAMBERT Academic Publishing, 2010

Synopsis

Let E be an elliptic curve defined over a number field K. An element of the n-Selmer group of E can be represented as a geometric object. Namely, as an everywhere locally soluble genus one curve defined by an equation of degree n. This equation is a generalised binary quartic when n=2, a ternary cubic when n=3, and two quadrics in four variables when n=4. By minimising these equations we mean making their invariants as small as possible. Unfortunately, the minimal (with the smallest invariants) equations of degree n are not unique in general. We exploit the theory of minimal regular models to find an alternative definition of minimality. Then we use this new definition to count the minimal equations of degree n.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Let E be an elliptic curve defined over a number field K. An element of the n-Selmer group of E can be represented as a geometric object. Namely, as an everywhere locally soluble genus one curve defined by an equation of degree n. This equation is a generalised binary quartic when n=2, a ternary cubic when n=3, and two quadrics in four variables when n=4. By minimising these equations we mean making their invariants as small as possible. Unfortunately, the minimal (with the smallest invariants) equations of degree n are not unique in general. We exploit the theory of minimal regular models to find an alternative definition of minimality. Then we use this new definition to count the minimal equations of degree n.

Biographie de l'auteur

Mohammad Sadek received his Ph.D. from Cambridge University in 2010. He is an assistant professor at the American University in Cairo. His research interests are in arithmetic of curves and their regular models.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
3843353840
ISBN 13 
9783843353847
Reliure
Broché
Nombre de pages
124
Coordonnées du fabricant
non disponible
Personne responsable
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