Thunderstones and Shooting Stars

Thunderstones and Shooting Stars

The Meaning of Meteorites

Book - 1986
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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.
Publisher: Cambridge, Mass. : Harvard University Press, 1986
ISBN: 9780674891371
0674891376
Branch Call Number: 523.51 D639t
QB755 .D63 1986
Characteristics: viii, 196 p. : ill. ; 25 cm

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