Timeline for A natural way of thinking of the definition of an Artin $L$-function?
Current License: CC BY-SA 4.0
6 events
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| Aug 8, 2023 at 0:21 | history | edited | KConrad | CC BY-SA 4.0 |
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| Apr 6, 2015 at 20:28 | comment | added | Sylvain JULIEN | @Will Sawin: do you mean a representation of $\mathbb{Z}$ or $\mathbb{Z}_{p}$ (or even $\hat{\mathbb{Z}}$)? My not-that-smartphone displays $\mathbb{Z}$ or $\mathbb{Z}$, which just can't be what you mean. | |
| Nov 8, 2012 at 1:53 | comment | added | Will Sawin | This "local representation" is not meant to imply anything $p$-adic. All I'm doing is using the fact that there is a well-defined up to conjugacy action of $Frob_p$, and viewing this action as a representation of $\mathbb Z$ or $\hat{\mathbb Z}$. The first half of the sentence was certainly known to him, as the definition doesn't make sense without it, and the second half is a very natural thing to do when you have the first. | |
| Nov 8, 2012 at 0:55 | comment | added | Filippo Alberto Edoardo | @Will: Nice answer. Do you think that your first point about local representations is historically coherent? I do not know the details, but Wikipedia says Artin introduced his function in 1923/4. By that time, was global CFT already thought idelically? Without that, or at least without a compatibility between local and global reciprocity laws, would you find it natural to "split a global representations into local ones" as it became customary later on? | |
| Nov 7, 2012 at 23:47 | comment | added | David Corwin | +1 for the last paragraph | |
| Nov 7, 2012 at 23:24 | history | answered | Will Sawin | CC BY-SA 3.0 |