Opened 5 years ago

Last modified 5 years ago

#16225 new defect

Divisors on curves should not only allow rational points

Reported by: pbruin Owned by:
Priority: major Milestone: sage-6.4
Component: algebraic geometry Keywords:
Cc: AlexGhitza Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Description

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.

Change History (2)

comment:1 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:2 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4
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