The Mathematical Institute, University of Oxford, Eprints Archive

Rational divisors in rational divisor classes

Bruin, N. and Flynn, E. V. (2004) Rational divisors in rational divisor classes. In: Algorithmic Number Theory. Lecture Notes in Computer Science, 3076 . Springer, Berlin, Germany, pp. 132-139. ISBN 3-540-22156-5



We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, which indicates how to compute this divisor in certain situations. We also discuss examples where C does not have points everywhere locally, and where no such K-rational divisor is contained in the K-rational divisor class.

Item Type:Book Section
Uncontrolled Keywords:Higher Genus Curves, Jacobians, Divisor Classes.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:254
Deposited By: E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:29 May 2015 18:18

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