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Lectures on Arakelov Geometry by C. Soule
Lectures on Arakelov Geometry by C. Soule
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Lectures on Arakelov Geometry

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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.
Release date Australia
September 15th, 1994
Audience
  • Professional & Vocational
Illustrations
1 Line drawings, unspecified
Pages
188
Dimensions
151x224x12
ISBN-13
9780521477093
Product ID
2362984

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