ENGLISH

Lectures on Arakelov Geometry

Book information

Publisher
Cambridge University Press
Year
1992
ISBN
0521416698, 9780521416696
LCC
QA242.5 .S68 1994
Language
english
Format
PDF
Filesize
3 MB (3090396 bytes)
Series
Cambridge Studies in Advanced Mathematics 33
Pages
185\185
Time added
2011-06-04 13:46:07

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 Soul?, 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.

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