Timeline for Finiteness of the volume of $G(F) \backslash G(\mathbb A)$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 5, 2021 at 20:34 | answer | added | user163485 | timeline score: 1 | |
| Jan 31, 2021 at 14:18 | vote | accept | D_S | ||
| Jan 31, 2021 at 2:12 | comment | added | Will Sawin | More precisely, wait between posting on one site and posting on another (so that the site with the best chance of answering gets a look at it first before the other ones have to) and link between the two posts (so that effort is not wasted on one site duplicating the work already done on another). | |
| Jan 31, 2021 at 2:09 | comment | added | Kimball | Please don't crosspost: math.stackexchange.com/q/4006223/11323 | |
| Jan 30, 2021 at 23:01 | answer | added | LSpice | timeline score: 3 | |
| Jan 30, 2021 at 22:52 | comment | added | D_S | I may not have represented the arguments I have seen correctly. Gelbart's book on the trace formula just says $$\int\limits_{G(F) \backslash G(\mathbb A)} dg \leq \int\limits_{\mathfrak S} dg < \infty$$ for which I tried to fill in the details with a "second isomorphism theorem" type argument. | |
| Jan 30, 2021 at 22:47 | comment | added | LSpice | I'm not sure what $(G(F) \cap \mathfrak S)\backslash\mathfrak S$ should mean; one cannot generally take a quotient by a subset. Perhaps simply identify points in $\mathfrak S$ that are $G(F)$-translates of one another; or perhaps just $G(F)\backslash G(F)\mathfrak S$. Anyway, if we take $\omega$ as in the definition of $\mathfrak S$ in your reference to be open (in $P_0(\mathbb A)$), then $\mathfrak S$ is open (in $G(\mathbb A)$), and that makes measures behave much more nicely. (EDIT: Hmm, we can't take it to be compact and open. This requires a bit more care, but should still work.) | |
| Jan 30, 2021 at 22:34 | history | asked | D_S | CC BY-SA 4.0 |