#16225: Divisors on curves should not only allow rational points
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.2
Component: algebraic geometry | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The class `sage.schemes.generic.divisor.Divisor_curve` should be extended
to allow divisors whose support does not just consist of rational points.
From the documentation of this class:
{{{
TODO: Divisors shouldn't be restricted to rational points. The
problem is that the divisor group is the formal sum of the group of
points on the curve, and there's no implemented notion of point on
`E/K` that has coordinates in `L`. This is what
should be implemented, by adding an appropriate class to
``schemes/generic/morphism.py``.
}}}
This is probably not exactly the right approach. For questions involving
arithmetic, it is better to define a divisor on a curve ''C'' over ''K''
to be a formal linear combination of prime divisors (= closed points of
the scheme). To obtain arbitrary linear combinations of points over an
extension field ''L'', as opposed to those that are "defined over K" in a
suitable sense, one should first base change to ''L''.
--
Ticket URL: <http://trac.sagemath.org/ticket/16225>
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