
Lectures on Arakelov Geometry
Cambridge University Press
Published on 15. September 1994
Book
Paperback/Softback
188 pages
978-0-521-47709-3 (ISBN)
Description
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 Soule, 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.
Reviews / Votes
"...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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
1 Line drawings, unspecified
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 11 mm
Weight
282 gr
ISBN-13
978-0-521-47709-3 (9780521477093)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

C. Soule | D. Abramovich | J. F. Burnol
Lectures on Arakelov Geometry
Book
06/1992
Cambridge University Press
€68.09
Article exhausted; check for reprint
Previous edition

C. Soule | D. Abramovich | J. F. Burnol
Lectures on Arakelov Geometry
Book
06/1992
Cambridge University Press
€68.09
Article exhausted; check for reprint
Persons
Author
Centre National de la Recherche Scientifique (CNRS), Paris
Princeton University, New Jersey
Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Leipzig
Content
Introduction; 1. Intersection theory on regular schemes; 2. Green currents; 3. Arithmetic Chow groups; 4. Characteristic classes; 5. The determinant of Laplace operators; 6. The determinant of the cohomology; 7. The curvature of the determinant line bundle; 8. The arithmetic Riemann-Roch-Grothendieck theorem; References; Index.