Timeline for Are there any simple, interesting consequences to motivate the local Langlands correspondence?
Current License: CC BY-SA 3.0
9 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| S Jun 16, 2014 at 18:16 | history | suggested | Jeremy Rouse |
Added a top-level tag (nt.number theory)
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| Jun 16, 2014 at 18:09 | review | Suggested edits | |||
| S Jun 16, 2014 at 18:16 | |||||
| Jun 16, 2014 at 18:02 | answer | added | Jeremy Rouse | timeline score: 13 | |
| Jun 15, 2014 at 10:29 | comment | added | user27920 | It can illuminate good & sst reduction properties of abelian varieties over number fields (via representation-theoretic criteria of Neron-Ogg-Shafarevich and Grothendieck). The last chapter of Katz-Mazur gives a geometric proof of surprising reduction properties for certain quotients of Jacobians with bad reduction. That proof (using vanishing cycles based on delicate bad reduction of modular curves) feels like a miracle. By contrast, LLC and local-global compatibility for GL$_2$ lead to an entirely different proof which, while not easy, doesn't have the feeling of a miracle. | |
| Jun 14, 2014 at 15:24 | answer | added | Marc Palm | timeline score: 5 | |
| Jun 14, 2014 at 15:21 | comment | added | user19918273 | I'm not literally asking for something like Taniyama-Shimura over local fields, just for some examples of convenient consequences to quote. It's entirely possible that there aren't really any that would be of partiuclar interest to a random mathematician and the applications are all technical properties of local fields. Either way, it'd be nice to know! | |
| Jun 14, 2014 at 15:16 | comment | added | Marc Palm | Is there a local version of the Taniyama-Shimura conjecture? Also it proves the Ramanujan conjecture in the global setting, but this does not apply to the local steting at all, where actually non-tempered things play a role. | |
| Jun 14, 2014 at 14:51 | history | asked | user19918273 | CC BY-SA 3.0 |