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| Deletions are marked like this. | Additions are marked like this. |
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| * Move functions out of abvar_modsym_factor into abvar and delete that file. | * (craig) Newforms issue: {{{ sage: f = CuspForms(37).newforms('a')[0] sage: f.coefficients(10) ------------------------------------ <type 'exceptions.TypeError'> Traceback (most recent call last) sage: f.coefficients([2..10]) ------------------------------------ <type 'exceptions.AttributeError'> Traceback (most recent call last) ... <type 'exceptions.AttributeError'>: 'Newform' object has no attribute '_compute' }}} |
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| * Torsion subgroups: * Refactor base class * Get implementation to work with defining data being (lattice, abvar); compute generators. |
* DONE (william) This is completely wrong (the modabvar function on modular symbols assumes it's ambient!): {{{ sage: m = ModularSymbols(37)[1] sage: m.modular_abelian_variety() Jacobian of the modular curve associated to the congruence subgroup Gamma0(37) }}} |
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| * Decomposition: | * DONE (william) Move functions out of abvar_modsym_factor into abvar and delete that file. * (william) Torsion subgroups: * (already done) Refactor base class * (done) Get implementation to work with defining data being (lattice, abvar); compute generators. * Quotients by finite subgroup * (william) Decomposition: |
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| * deprecate hecke_decomposition * label function * create from label |
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| * Label function | * (craig) Implement {{{f.number()}}} for f a newform. |
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| * Create from label | * (craig) 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)}}}. |
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| * Create a small mock database | * (craig) abelian varieties should cache their ambient modular abelian variety |
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| * 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)}}}. | * (craig) Compute End(A): * for simple $A_f$ (DONE) * in general. * disc of it. * ideals and annihilators * order in a ring of integers (for A simple) * given a ring R in EndAlg(A) where every element has integral charpoly, find an isogenous abelian variety with End(A) = R. * explicit isomorphism between HeckeAlgebra sitting in End(A) and a commutative ring * base extension of End(A) |
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| * Compute End(A) in general. | * (craig) Degeneracy maps |
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| * Morphisms: | * (william/craig) Morphisms: |
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* (william/craig) Isogenies: * Complementary -- invert matrix, clear denom. * Dual |
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| * Quotients by finite subgroup | * (william) Intersection pairing |
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| * Intersection pairing | * (?) Poincare Reducibility: * projection * quotients by abelian subvariety |
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| * Poincare Reducibility: * projection |
* (craig/william) Minimal isogeny degree for A, B simple. |
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| * Quotients by abelian subvariety * Minimal isogeny degree for A, B simple. |
* (craig/william) Create a small mock database |
Modular Abelian Varieties
Todo on March 16
- (craig) Newforms issue:
sage: f = CuspForms(37).newforms('a')[0] sage: f.coefficients(10) ------------------------------------ <type 'exceptions.TypeError'> Traceback (most recent call last) sage: f.coefficients([2..10]) ------------------------------------ <type 'exceptions.AttributeError'> Traceback (most recent call last) ... <type 'exceptions.AttributeError'>: 'Newform' object has no attribute '_compute'
- DONE (william) This is completely wrong (the modabvar function on modular symbols assumes it's ambient!):
sage: m = ModularSymbols(37)[1] sage: m.modular_abelian_variety() Jacobian of the modular curve associated to the congruence subgroup Gamma0(37)
- DONE (william) Move functions out of abvar_modsym_factor into abvar and delete that file.
- (william) Torsion subgroups:
- (already done) Refactor base class
- (done) Get implementation to work with defining data being (lattice, abvar); compute generators.
- Quotients by finite subgroup
- (william) Decomposition:
- three types:
- ungrouped as simple abvars (default)
- groups abvars
- over End(A)
- deprecate hecke_decomposition
- label function
- create from label
- three types:
(craig) Implement f.number() for f a newform.
(craig) 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).
- (craig) abelian varieties should cache their ambient modular abelian variety
- (craig) Compute End(A):
for simple A_f (DONE)
- in general.
- disc of it.
- ideals and annihilators
- order in a ring of integers (for A simple)
given a ring R in EndAlg(A) where every element has integral charpoly, find an isogenous abelian variety with End(A) = R.
explicit isomorphism between HeckeAlgebra sitting in End(A) and a commutative ring
- base extension of End(A)
- (craig) Degeneracy maps
- (william/craig) Morphisms:
- Kernels
- Cokernels
- (william/craig) Isogenies:
- Complementary -- invert matrix, clear denom.
- Dual
- (william) Intersection pairing
- (?) Poincare Reducibility:
- projection
- quotients by abelian subvariety
- (craig/william) Minimal isogeny degree for A, B simple.
- (craig/william) Create a small mock database
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