Lectures on Arakelov Geometry (Cambridge Studies in Advanced Mathematics, Series Number 33) - Hardcover

Soulé, C.; Abramovich, D.; Burnol, J. F.; Kramer, J. K.

Hardcover

ISBN 10: 0521416698 ISBN 13: 9780521416696

Publisher: Cambridge University Press, 1992

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.

About this title

Review

"...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

Book Description

An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory. This text is based on a graduate course given at Harvard University and is aimed at number theorists and algebraic geometers. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1992
• Language: English
• ISBN 10: 0521416698
• ISBN 13: 9780521416696
• Binding: Hardcover
• Edition number: 1
• Number of pages: 185