#17869: prove_BSD for elliptic curve uses an incorrect lemma
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Reporter: wuthrich | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: elliptic curves | Resolution:
Keywords: BSD | Merged in:
Authors: Chris Wuthrich | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/wuthrich/ticket/17869 | 8b6a73af07a1c0829a09133a0af9fcef1b724eee
Dependencies: | Stopgaps:
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Changes (by wuthrich):
* status: new => needs_review
Old description:
> Let E be an elliptic curve over Q. For certain primes p, the function
> prove_BSD will make reference to the paper of Stein et al on the
> numerical verification of BSD. Unfortunately, the Theorem 5.3 in there is
> incorrect. The condition that the H 1 vanishes is computed wrong in their
> Lemma 5.4.
>
> As a consequence, sage sometimes claims that we know how to prove BSD
> when the verification is in fact much harder and rules out some cases
> when we would know it.
>
> The patch here replaces the condition with a new condition, based on a
> paper I am writing with Taylor Lawson. We explicitly find when the
> cohomology groups in questions do not vanish. I will point to the paper
> when it is ready.
>
> I wait with asking for review until then.
New description:
Let E be an elliptic curve over Q. For certain primes p, the function
prove_BSD will make reference to the paper of Stein et al on the numerical
verification of BSD. Unfortunately, the Theorem 5.3 in there is incorrect.
The condition that the H 1 vanishes is computed wrong in their Lemma 5.4.
As a consequence, sage sometimes claims that we know how to prove BSD when
the verification is in fact much harder and rules out some cases when we
would know it.
The patch here replaces the condition with a new condition, based on a
paper I have written with Taylor Lawson: http://arxiv.org/abs/1505.02940 .
--
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Ticket URL: <http://trac.sagemath.org/ticket/17869#comment:5>
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