By C. Soulé,D. Abramovich,J. F. Burnol,J. K. Kramer

ISBN-10: 0521416698

ISBN-13: 9780521416696

ISBN-10: 0521477093

ISBN-13: 9780521477093

Arakelov thought is a brand new geometric method of diophantine equations. It combines algebraic geometry within the experience of Grothendieck with subtle analytic instruments corresponding to currents on advanced manifolds and the spectrum of Laplace operators. it's been utilized by Faltings and Vojta of their proofs of remarkable conjectures in diophantine geometry. This account provides the paintings of Gillet and Soulé, extending Arakelov geometry to raised dimensions. It encompasses a facts of Serre's conjecture on intersection multiplicities and an mathematics Riemann-Roch theorem. to help quantity theorists, historical past fabric on differential geometry is defined, yet recommendations from algebra and research are coated in addition. numerous open difficulties and examine issues also are pointed out. The e-book relies on lectures given at Harvard collage and is aimed toward graduate scholars and researchers in quantity concept and algebraic geometry. advanced analysts and differential geometers also will locate in it a transparent account of modern effects and purposes in their topics to new areas.

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Lectures on Arakelov Geometry (Cambridge Studies in Advanced Mathematics) by C. Soulé,D. Abramovich,J. F. Burnol,J. K. Kramer


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