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Lectures on Arakelov geometry

Soule, C.

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Lectures on Arakelov geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on Arakelov geometry/ C. Soule, written with D. Abramovich, J.-F. Burnol & J. Kramer.
Author:	Soule, C.
Published:	Cambridge :Cambridge University Press, : 1994.,
Description:	vi, 177 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Arakelov theory. -
Online resource:	https://doi.org/10.1017/CBO9780511623950
ISBN:	9780511623950

Lectures on Arakelov geometry
Soule, C.

Lectures on Arakelov geometry[electronic resource] /C. Soule, written with D. Abramovich, J.-F. Burnol & J. Kramer. - Cambridge :Cambridge University Press,1994. - vi, 177 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;33. - Cambridge studies in advanced mathematics ;33..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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. The book is based on lectures given at Harvard University and is aimed at graduate students and researchers in number theory and algebraic geometry. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.

ISBN: 9780511623950Subjects--Topical Terms:

728392
Arakelov theory.

LC Class. No.: QA242.5 / .S68 1994

Dewey Class. No.: 516.35

Lectures on Arakelov geometry
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245 1 0 $a Lectures on Arakelov geometry $h [electronic resource] / $c C. Soule, written with D. Abramovich, J.-F. Burnol & J. Kramer.
260 $a Cambridge : $b Cambridge University Press, $c 1994.
300 $a vi, 177 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 33
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a 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. The book is based on lectures given at Harvard University and is aimed at graduate students and researchers in number theory and algebraic geometry. Complex analysts and differential geometers will also find in it a clear account of recent results and applications of their subjects to new areas.
650 0 $a Arakelov theory. $3 728392
830 0 $a Cambridge studies in advanced mathematics ; $v 33. $3 3470571
856 4 0 $u https://doi.org/10.1017/CBO9780511623950