Timeline for How to determine $O(L)$ is finite or not?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Oct 26, 2013 at 2:09 | answer | added | WKC | timeline score: 4 | |
| Aug 6, 2013 at 16:52 | comment | added | Will Jagy | @user36938, understood | |
| Aug 6, 2013 at 15:04 | comment | added | user36938 | @Will: Someone fortunate enough to be a graduate student at Harvard has many people nearby to speak with in person about things like that. (For a slick proof, he should make more effective use of the fact that any two adelic lattices are commensurable with each other, and that tensoring against $\widehat{\mathbf{Z}}$ has no effect on the "lattice" of finite-index subgroups.) | |
| Aug 6, 2013 at 14:23 | comment | added | Will Jagy | @user36938, you might like this question on the other site, math.stackexchange.com/questions/459064/adelic-lattices The kid asking is a graduate student at Harvard and might well start using MO... | |
| Aug 6, 2013 at 4:51 | comment | added | Will Jagy | @user36938, thanks. There are times that I wish I had actually studied the full theory. Lots of stuff I like is written in adelic language, probably starting with Kneser 1961. | |
| Aug 6, 2013 at 4:38 | comment | added | user36938 | @Will: In all dimensions $\ge 3$ it has to be infinite: the special orthogonal and spin groups are always semisimple (even if not absolutely simple for dimension 4), so one can apply strong approximation relative to the infinite place for the simply connected spin group and open subset of its finite-adelic points corresponding to the $\widehat{\mathbf{Z}}$-points relative to the $\mathbf{Z}$-structure provided by the lattice (which gives a $\mathbf{Z}$-structure to the Clifford algebra and hence to the spin group, thereby making sense of the $\widehat{\mathbf{Z}}$-points just mentioned). | |
| Aug 5, 2013 at 23:29 | comment | added | Will Jagy | I have no idea how any of these could be finite. Indefinite binary forms (nonsquare discriminant) have infinite groups, here you have at least total dimension 4. If you have any finite examples, please let me know. | |
| Aug 5, 2013 at 21:00 | review | First posts | |||
| Aug 5, 2013 at 21:11 | |||||
| Aug 5, 2013 at 20:57 | history | edited | Andrew | CC BY-SA 3.0 |
added 3 characters in body
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| Aug 5, 2013 at 20:45 | history | asked | Andrew | CC BY-SA 3.0 |