Articles liés à Lectures on Arakelov Geometry

Lectures on Arakelov Geometry - Couverture souple

Livre 9 sur 151: Cambridge Studies in Advanced Mathematics

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9780521477093: Lectures on Arakelov Geometry
Couverture souple
ISBN 10 : 0521477093 ISBN 13 : 9780521477093
Editeur : Cambridge University Press, 2008

Synopsis

Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has been used by Faltings and Vojta in their proofs of outstanding conjectures in diophantine geometry. This account presents the work of Gillet and Soulé, extending Arakelov geometry to higher dimensions. It includes a proof of Serre's conjecture on intersection multiplicities and an arithmetic Riemann-Roch theorem. To aid number theorists, background material on differential geometry is described, but techniques from algebra and analysis are covered as well. Several open problems and research themes are also mentioned. The book is based on lectures given at Harvard University and is aimed at graduate students and researchers in number theory and algebraic geometry. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.

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

Présentation de l'éditeur

Arakelov theory is a new geometric approach to diophantine equations. It combines algebraic geometry in the sense of Grothendieck with refined analytic tools such as currents on complex manifolds and the spectrum of Laplace operators. It has been used by Faltings and Vojta in their proofs of outstanding conjectures in diophantine geometry. This account presents the work of Gillet and Soulé, extending Arakelov geometry to higher dimensions. It includes a proof of Serre's conjecture on intersection multiplicities and an arithmetic Riemann-Roch theorem. To aid number theorists, background material on differential geometry is described, but techniques from algebra and analysis are covered as well. Several open problems and research themes are also mentioned. The book is based on lectures given at Harvard University and is aimed at graduate students and researchers in number theory and algebraic geometry. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.

Revue de presse

"...has been written with great care, is very enjoyable to read and could be recommended to anyone interested in this important area." Dipendra Prasad, Mathematical Reviews

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

Éditeur
Cambridge University Press
Date d'édition
2008
Langue
anglais
ISBN 10 
0521477093
ISBN 13 
9780521477093
Reliure
Broché
Nombre de pages
188
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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