Abstract
The purpose of this part is to give an introduction to intersection theory on arithmetic surfaces, a theory initiated by S.Yu Arakelov in [A1,2,3] and further developped by G. Faltings in [F]. The idea, propagated during the last years in particular by L. Szpiro, is roughly to replace or better to enrich algebro-geometric structures at the infinite primes involved by hermitian structures as for example hermitian line bundles, curvatures, volumes etc.
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References
S. Arakelov: Families of curves whith fixed degeneracies, Izv. Akad. Nauk. 35., 1971, 1269–1293.
S. Arakelov: An intersection theory for divisors on an arithmetic surface, Izv. Akad. Nauk 38, 1974, 1179–1192.
S. Arakelov: Theory of Intersections on the Arithmetic surface, Proc. Int. Congress Vancouver, 1974, 405–408.
G. Faltings: Calculus on arithmetic surfaces, Annals of Math., 1984, to appear.
G. Faltings: Properties of Arakelov’s Intersection product. SLN 997, p 138–146.
Ph. Griffith, Principles of algebraic Geometry, J. Harris: New York, 1978.
D. Quillen: Determinants of ∂-operators, Vortrag auf der Bonner Arbeitstagung 1982.
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© 1984 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Stuhler, U. (1984). Intersection Theory on Arithmetic Surfaces. In: Rational Points. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-83918-3_7
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DOI: https://doi.org/10.1007/978-3-322-83918-3_7
Publisher Name: Vieweg+Teubner Verlag
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