Timeline for Why should the anabelian geometry conjectures be true?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2012 at 2:22 | vote | accept | CommunityBot | ||
| Feb 4, 2012 at 2:22 | history | bounty ended | Makhalan Duff | ||
| Nov 14, 2011 at 11:06 | history | edited | Robert Kucharczyk | CC BY-SA 3.0 |
Incorporated comment
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| Nov 14, 2011 at 10:50 | comment | added | Torsten Ekedahl | Note that in the genus $1$ case you do not recover the elliptic curve from its Tate modules. If you twist a (CM-)curve by a rank $1$ projective module over its endomorphism ring then the result will have the same Tate modules but only be isomorphic to the curve if the module is free. The same in some sense holds true in higher genus only that the twists may not be Jacobians. Hence it is crucial to look at the fundamental group and not its abelianisation. | |
| Nov 13, 2011 at 13:25 | comment | added | Robert Kucharczyk | Nothing, and that is why I think my "answer" misses the point somehow. What I was thinking about is what Deligne does in Le groupe fondamental ..., and there he writes in the introduction that this theory is far away from Grothendieck's anabelian dream, but instead his philosophy of motives can be applied ... I'm still eager to see someone with more knowledge about these things give an answer to your question. | |
| Nov 12, 2011 at 16:11 | comment | added | Makhalan Duff | That's interesting, thanks. I do wonder though, harking back to Torsten's comment, what in this argument uses the fact that $X$ is hyperbolic. | |
| Nov 12, 2011 at 11:55 | history | edited | Robert Kucharczyk | CC BY-SA 3.0 |
formatting improved
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| Nov 12, 2011 at 11:49 | history | answered | Robert Kucharczyk | CC BY-SA 3.0 |