Timeline for Is the following the right definition of $L$-functions (on the Galois side)?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2013 at 21:54 | comment | added | Will Sawin | "that quotient = $\hat{\mathbb Z}$. | |
| Feb 3, 2013 at 21:53 | comment | added | Will Sawin | The ramification subgroups of the Galois group. The map $Gal(\mathbb Q_p) = Gal(\mathbb Q)$ is defined up to conjugacy. There is an extension $1 \to I\to Gal(\mathbb Q_p) \to \hat{\mathbb Z} \to 1$ for a subgroup $I$ called the inertia or ramification group. The Frobenius element is the generator of that quotient. On any representation on which $I$ acts trivially, there is a well-defined conjugacy class of Frobenius, with a well-defined characteristic polynomial. | |
| Feb 3, 2013 at 21:22 | comment | added | Nicole | The second part of your answer makes perfect sense to me. Can you explain a little more (or point me to a place that explains) the first part of your answer? Ramification of what over what? | |
| Feb 3, 2013 at 20:55 | history | answered | Will Sawin | CC BY-SA 3.0 |