#16959: p-primary bound for Sha can be improved
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Reporter: wuthrich | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Keywords: tate-shafarevich, shark
Merged in: | Authors: Chris Wuthrich
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This ticket aims to improve the p-adic bit of sha_tate for elliptic curves
over Q.
* There are a few minor points to improve in the documentation (some of
the conditions are not stated precisely or slightly wrong).
* We can now allow reducible primes, too. Since #6406 we ask for the
p-adic rep to be surjective. However the recent results in [1] imply that
the bounds are also correct for all odd primes of semi-stable reduction
when the curve admits a p-isogeny.
* There is a small bug in padic_lseries, which made this fails:
{{{
sage: E = EllipticCurve("5040bi1")
sage: E.sha().p_primary_bound(5)
}}}
(reported by Charlene Soh).
[1] C Wuthrich, On the integrality of modular symbols and Kato's Euler
system for elliptic curves. Doc. Math. 19 (2014), 381–402.
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Ticket URL: <http://trac.sagemath.org/ticket/16959>
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