#18614: Abelian variety constructor needs sanity checks
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Reporter: davidloeffler | Owner:
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-6.8
Component: modular forms | Keywords: abelian varieties
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Sage can create abelian varieties attached to modular symbol spaces.
Sadly, the output is often mathematically nonsensical, because the
construction only makes sense when the weight is 2 but this is not checked
in the constructor:
{{{
sage: AbelianVariety(ModularSymbols(23, 6).cuspidal_submodule())
Abelian subvariety of dimension 9 of J0(23)
sage: J0(23).dimension()
2
}}}
There are other related bugs: even for weight 2, the construction only
makes sense when the modular symbol space is defined over QQ, but the
constructor accepts arbitrary modular symbol spaces, resulting in objects
so badly broken that they can't even represent themselves as strings:
{{{
sage: chi = DirichletGroup(33).1^2
sage: M = ModularSymbols(chi).cuspidal_submodule()
sage: M1, M2 = M.decomposition()
sage: A = AbelianVariety(M1)
sage: A
<repr(<sage.modular.abvar.abvar.ModularAbelianVariety_modsym_with_category
at 0x7fcf67a3b368>) failed: NotImplementedError>
}}}
Moreover, the handling of "base ring" is totally misleading:
{{{
sage: M = ModularSymbols(23, 2, base_ring=QQbar).cuspidal_submodule()
sage: A=AbelianVariety(M); A
Abelian variety J0(23) over Algebraic Field of dimension 2
sage: A.base_ring()
Algebraic Field
}}}
This suggests that A is the base-extension to QQbar of the Q-variety
J0(23); but it's not -- base-extending the abelian variety as a variety
has nothing to do with base-extending the defining modular symbols space!
William: I'm ccing you on this ticket because you were the last person to
do actual mathematical work on abelian varieties in Sage (in 2010) --
everything more recent in the git logs is just general Sage-wide bug-
fixing.
--
Ticket URL: <http://trac.sagemath.org/ticket/18614>
Sage <http://www.sagemath.org>
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