Lectures on Arakelov Geometry
C. Soule, D. Abramovich, J. F. Burnol, J. K. Kramer
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 Soul?, 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.
Tahun:
1992
Penerbit:
Cambridge University Press
Bahasa:
english
Halaman:
185
ISBN 10:
0521416698
ISBN 13:
9780521416696
Nama siri:
Cambridge Studies in Advanced Mathematics 33
Fail:
PDF, 2.95 MB
IPFS:
,
english, 1992
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