#16708: Class group part of the Selmer group of a number field is incorrectly
computed
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: number fields | Keywords: Selmer group
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The construction of elements of the ''m''-Selmer group of a number field
from elements of the ''m''-torsion of the class group uses an incorrect
formula, as the following example shows:
{{{
sage: K.<a> = QuadraticField(-5)
sage: p = K.primes_above(2)[0]
sage: S = K.selmer_group((), 4)
sage: all(4.divides(x.valuation(p)) for x in S)
False # should be True
}}}
The class group is cyclic of order 2, generated by the unique prime ideal
''p'' above 2. To construct an element of the ''m''-Selmer group from it,
for ''m'' even, one has to take a generator of the principal ideal
''p^m^''. However. the `selmer_group()` method currently uses a generator
of ''p''^2^ for any even ''m''.
--
Ticket URL: <http://trac.sagemath.org/ticket/16708>
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