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Lectures on Arakelov Geometry

Lectures on Arakelov Geometry - Cambridge Studies in Advanced Mathematics

Paperback (15 Sep 1994)

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Publisher's 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 the Publisher

Cambridge University Press

Cambridge University Press dates from 1534 and is part of the University of Cambridge. We further the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

Book information

ISBN: 9780521477093
Publisher: Cambridge University Press
Imprint: Cambridge University Press
Pub date:
DEWEY: 516.3/5
DEWEY edition: 22
Language: English
Number of pages: 188
Weight: 310g
Height: 155mm
Width: 229mm
Spine width: 18mm