Timeline for Is the Modularity Theorem (currently) effective?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 15, 2017 at 13:53 | comment | added | user19475 | I think Mordell is a consequence of Shafarevich, not vice versa. | |
| Mar 2, 2014 at 13:35 | history | edited | Colin McLarty | CC BY-SA 3.0 |
Clarified an issue.
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| Mar 2, 2014 at 2:49 | vote | accept | Colin McLarty | ||
| Mar 2, 2014 at 2:43 | comment | added | Qiaochu Yuan | Yes, Sage can do it. First, it can find a basis of the appropriate space of forms (sagemath.org/doc/reference/modfrm/sage/modular/modform/…). Second, it can compute the action of the Hecke operators on this basis (sagemath.org/doc/reference/modfrm/sage/modular/modform/…), so you can diagonalize this action. | |
| Mar 2, 2014 at 2:40 | comment | added | Colin McLarty | Yes of course searching a finite list is effective. Do we have an effective way to create the finite list? | |
| Mar 2, 2014 at 2:39 | comment | added | Qiaochu Yuan | In this case there's no obstacle to searching the space, since the list of eigenforms is finite and we know how to find it. (Right?) | |
| Mar 2, 2014 at 2:38 | answer | added | Noam D. Elkies | timeline score: 31 | |
| Mar 2, 2014 at 2:37 | comment | added | Colin McLarty | Non-effectiveness is no obstacle to validity of the proof. But I wonder if current proofs are effective. | |
| Mar 2, 2014 at 2:33 | comment | added | Qiaochu Yuan | The non-effectiveness of the proof is not necessarily an obstacle. The proof guarantees that a certain search (namely, if I'm not horribly mistaken, the search for a cuspidal eigenform with the right Fourier coefficients) will return a result, but one can perform this search knowing that it's going to return a result without worrying about why one knows it's going to return a result (because the appropriate space of forms, for fixed $N$, is finite-dimensional). Right? | |
| Mar 2, 2014 at 2:18 | history | asked | Colin McLarty | CC BY-SA 3.0 |