|
Size: 1037
Comment:
|
Size: 2841
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 6: | Line 6: |
| * 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' }}} |
| Line 8: | Line 19: |
| * 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) }}} |
| Line 12: | Line 26: |
| * 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: |
| Line 17: | Line 38: |
| * deprecate hecke_decomposition * label function * create from label |
|
| Line 18: | Line 42: |
| * Label function | * (craig) Implement {{{f.number()}}} for f a newform. |
| Line 20: | Line 44: |
| * 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)}}}. |
| Line 22: | Line 46: |
| * Create a small mock database | * (craig) abelian varieties should cache their ambient modular abelian variety |
| Line 24: | Line 48: |
| * 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 $A_f$ * 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) |
| Line 26: | Line 58: |
| * Compute End(A) in general. | * (craig) Degeneracy maps |
| Line 28: | Line 60: |
| * Morphisms: | * (william/craig) Morphisms: |
| Line 31: | Line 63: |
* (william/craig) Isogenies: * Complementary -- invert matrix, clear denom. * Dual |
|
| Line 32: | Line 68: |
| * Quotients by finite subgroup | * (william) Intersection pairing |
| Line 34: | Line 70: |
| * Intersection pairing | * (?) Poincare Reducibility: * projection * quotients by abelian subvariety |
| Line 36: | Line 74: |
| * Poincare Reducibility: * projection |
* (craig/william) Minimal isogeny degree for A, B simple. |
| Line 39: | Line 76: |
| * Quotients by abelian subvariety * Minimal isogeny degree for A, B simple. |
* (craig/william) Create a small mock database |
| Line 46: | Line 80: |
| == Todo on March 17 == | == Todo on Monday, March 17 == |
| Line 48: | Line 82: |
| * 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
- (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
- 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