Lectures on Arakelov Geometry (Paperback) (ISBN-13: 9780521477093)

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.

Author: C. Soule, J. F. Burnol, D. Abramovich
ISBN-10: 0521477093
ISBN-13: 9780521477093
Publisher: Cambridge University Press
Language: English
Published: 09/15/1994
Pages: 188
Format: Paperback
Weight: 0.59lbs
Size: 8.80h x 5.91w x 0.40d