A Pairing on the Group of Degree Zero Divisors of a Curve Over a Number Field
Pairing Construction on Degree Zero Divisors of a Curve over a Number Field with Arakelov Geometry
by Shweta*,
- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659
Volume 3, Issue No. 5, May 2012, Pages 0 - 0 (0)
Published by: Ignited Minds Journals
ABSTRACT
In this paper we construct a pairingon the group of degree zero divisors of a curve over a number field. This isaccomplished by passing from divisors of the curve to divisors of an associatedscheme and then employing an Arakelov intersection theory. Arakelov geometrystudies a scheme X over the ring of integers Z, by putting Hermitian metrics onholomorphic vector bundles over X(C), the complex points of X. This extraHermitian structure is applied as a substitute, for the failure of the schemeSpec(Z) to be a complete variety..
KEYWORD
pairing, group, degree zero divisors, curve, number field, divisors, associated scheme, Arakelov intersection theory, Arakelov geometry, complete variety
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