Timeline for Why locally algebraic characters of $\text{Gal}(\overline{\mathbb Q}/\mathbb Q)$ are associated to $A_0$ Grossencharacters/algebraic Hecke characters?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 23 at 20:43 | comment | added | Will Sawin | @JoseCanseco One can check indirectly that the final character ends up being continuous. The point is the original character is finitely ramified so after passing to an open subgroup of the ideles it agrees with the $n$th power of the $\mathbb Z_\ell$ component. So when you multiply and divide, after restricting to the open subgroup you get the $n$th power of the $\mathbb R$ component, which is continuous. Since it's continuous on an open subgroup it's continuous on every coset of that open subgroup and thus continuous everywhere. | |
| May 23 at 18:13 | comment | added | JoseCanseco | Can I do it in a continuous way? | |
| May 23 at 17:59 | comment | added | Will Sawin | @JoseCanseco Well, one can just embed $E_\lambda$ into $\mathbb C$. | |
| May 23 at 17:47 | comment | added | JoseCanseco | Why do we know that the image is inside $\mathbb C$ and not in $E_{\lambda}$? Because otherwise I cannot multiply by the $\mathbb R$ component. | |
| Apr 22 at 13:18 | history | answered | Will Sawin | CC BY-SA 4.0 |