Timeline for "Purely local" proof of local Langlands
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 14, 2012 at 4:41 | comment | added | natura | @Jared, Thanks! | |
| May 14, 2012 at 4:40 | vote | accept | natura | ||
| May 14, 2012 at 3:27 | comment | added | Jared Weinstein | @Jef: Yes, the existence of $f$ is proved by purely local means in Chapter 1 of the Arthur-Clozel book on base change. That result is used to characterize automorphic base change. On the other hand, [AC] uses global means to establish the existence of automorphic base change. | |
| May 13, 2012 at 20:00 | comment | added | Jef | @Jared : on the "other side of Scholze's formula", there is the trace of a certain "test function", say $f$. The latter function is obtained by "base change transfer" from another function $\phi$. While $\phi$ is undoubtedly purely local (involves cohomology of some deformation space for p-divisible groups), and while $f$ is characterized by purely local conditions (matching of orbital integrals), I wonder if the very existence of $f$ has been proved by local means ??? | |
| May 12, 2012 at 12:12 | comment | added | Rob Harron | Ah, I didn't know Scholze had a local characterization. It's very satisfying that it's in terms of something that pins down the representation of the Weil group using traces, rather than $L$- and $\epsilon$-factors. | |
| May 12, 2012 at 4:22 | history | answered | Jared Weinstein | CC BY-SA 3.0 |