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

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## Abstract

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 |
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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: | 20 Jul 2009 14:19 |

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