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Lectures on Arakelov Geometry by C. Soule, J. F. Burnol, D. Abramovich

Lectures on Arakelov Geometry

by C. Soule , J. F. Burnol , D. Abramovich
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Book cover type: Paperback
  • ISBN13: 9780521477093
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 188
  • Original Price: GBP 55.0
  • Language: English
  • Edition: Revised
  • Item Weight: 268 grams
  • BISAC Subject(s): Geometry / Algebraic

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.

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