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Divisors on curves should not only allow rational points #16225

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pjbruin opened this issue Apr 24, 2014 · 0 comments
Open

Divisors on curves should not only allow rational points #16225

pjbruin opened this issue Apr 24, 2014 · 0 comments

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@pjbruin
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pjbruin commented Apr 24, 2014

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.

CC: @aghitza

Component: algebraic geometry

Issue created by migration from https://trac.sagemath.org/ticket/16225

@pjbruin pjbruin added this to the sage-6.2 milestone Apr 24, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014
@sagetrac-vbraun-spam sagetrac-vbraun-spam mannequin modified the milestones: sage-6.3, sage-6.4 Aug 10, 2014
@mkoeppe mkoeppe removed this from the sage-6.4 milestone Dec 29, 2022
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