Lectures on Arakelov Geometry (Paperback, Revised)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	Cambridge Studies in Advanced Mathematics
Release date:	September 1994
First published:	1992
Authors:	C. Soule • D. Abramovich • J. F. Burnol • J. K. Kramer
Dimensions:	224 x 151 x 12mm (L x W x T)
Format:	Paperback - Trade
Pages:	188
Edition:	Revised
ISBN-13:	978-0-521-47709-3
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	0-521-47709-3
Barcode:	9780521477093

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