Timeline for Local splitting of modular Galois representations as $p$ varies
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 16, 2012 at 12:46 | comment | added | Arijit | Here is a nice exposition of Ghate's results: www-ma2.upc.edu/vrotger/docs/students/FCastella.pdf | |
| Feb 15, 2012 at 11:12 | comment | added | unramified | The conjecture is attributed to Ralph Greenberg although Eknath Ghate and Nike Vatsal have done the most work on it. One can find 3 or 4 papers on work related to this problem on Ghate's page. Emerton has quite a famous preprint "A p-adic variational Hodge conjecture and modular forms with complex multiplication" where he shows how this conjecture follows from the conjecture in the title of the paper. | |
| Feb 15, 2012 at 10:41 | comment | added | David Loeffler | @Dror: I've seen this conjecture in papers of Pollack and Stevens on p-adic modular symbols; I don't know if that's where it first originated. | |
| Feb 15, 2012 at 9:04 | comment | added | Dror Speiser | Oh wow, I haven't heard of this "split implies CM" conjecture. Is there some reference to this? Maybe a name? | |
| Feb 15, 2012 at 6:29 | comment | added | unramified | Thanks monodromy. Could you possibly expand on the equivalence using Cebotarev (a reference perhaps?) | |
| Feb 15, 2012 at 4:03 | comment | added | monodromy | Your proposed equivalence obviously amounts to one implication, and this is expected by the reason that you say, and in fact, by an application of Cebotarev (I believe) equivalent to the "splitting implies CM" conjecture. So the answer to your question would be: it is expected that to be so (i.e. true), but apparently no one knows yet how to prove it in general. | |
| Feb 14, 2012 at 23:32 | history | asked | unramified | CC BY-SA 3.0 |