Opened 12 years ago

#11039 new enhancement

Write a framework for computing with Galois cohomology classes.

Reported by: Jamie Weigandt Owned by: Jamie Weigandt
Priority: major Milestone: sage-feature
Component: number theory Keywords: galois cohomology, Selmer groups
Cc: William Stein, John Cremona, Robert Miller, wuthrich Merged in:
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Report Upstream: N/A Work issues:
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There are several independent algorithms which compute various Selmer groups associated to elliptic curves. Unfortunately, none of them interact very well. You can't piece together partial information given by mwrank with partial information given by Simon's two_descent scripts. You also cannot modify the local conditions used to compute the relevant Selmer groups to investigate Kolyvagin systems.

We need to create at Galois cohomology class in Sage that can pointed to by as much of the existing code that computes Shafarevich-Tate groups, Kolyvagin classes, Selmer groups, and principal homogenous spaces as possible, while more importantly forming a backdrop to implement more of this functionality, such especially Kolyvagin classes and higher descents, in a consistent and elegant way.

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