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⇤ ← Revision 1 as of 2008-03-16 22:55:00
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| Deletions are marked like this. | Additions are marked like this. |
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| == Todo on March 17 == | == Todo on Monday, March 17 == |
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| * Optimize decomposition | * Write doctests, etc., for everything above. * Optimize everything == Todo on Tuesday, March 18 == * Write paper == Todo on Wednesday, March 19 == * Write paper |
Modular Abelian Varieties
Todo on March 16
- Move functions out of abvar_modsym_factor into abvar and delete that file.
- Torsion subgroups:
- Refactor base class
- Get implementation to work with defining data being (lattice, abvar); compute generators.
- Decomposition:
- three types:
- ungrouped as simple abvars (default)
- groups abvars
- over End(A)
- three types:
- Label function
- Create from label
- Create a small mock database
Compute the Hecke algebra image in End(A) and find a good clean way to represent for Hecke stable. New object that is a subring of End(A). Have methods like R.index_in(S).
- Compute End(A) in general.
- Morphisms:
- Kernels
- Cokernels
- Quotients by finite subgroup
- Intersection pairing
- Poincare Reducibility:
- projection
- Quotients by abelian subvariety
- Minimal isogeny degree for A, B simple.
Todo on Monday, March 17
- Write doctests, etc., for everything above.
- Optimize everything
Todo on Tuesday, March 18
- Write paper
Todo on Wednesday, March 19
- Write paper