Timeline for Q-lattices and commensurability, any insight into the definition and intuition?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2010 at 12:55 | vote | accept | mebassett | ||
| Aug 10, 2010 at 23:21 | history | edited | Gerry Myerson | CC BY-SA 2.5 |
improved formatting
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| Aug 10, 2010 at 21:24 | comment | added | Kevin Ventullo | For condition 1, the lattices don't have to be rational multiples of each other, e.g. take $\Lambda_1=\langle(1,0),(0,1)\rangle$, $\Lambda_2=\langle(\frac{1}{2},0),(0,2)\rangle$. They just have to be contained in the same $n$-dimensional $\mathbb{Q}$-vector space. Equivalently, there exist integers $N$ and $M$ so that $M\Lambda_1\subset\Lambda_2$ and $N\Lambda_2\subset\Lambda_1$. | |
| Aug 10, 2010 at 19:34 | comment | added | mebassett | Connes & Marcolli, Noncommutative Geometry, Quantum Fields, and Motives. Marcolli, Lectures on Arithmetic Noncommutative Geometry. Various other papers from those two. alainconnes.org/docs/Qlattices.pdf is a short one. Thanks for the comments on the notation, very helpful. | |
| Aug 10, 2010 at 18:17 | answer | added | Torsten Ekedahl | timeline score: 3 | |
| Aug 10, 2010 at 18:04 | comment | added | Victor Protsak | Can you, please, give a reference to the paper where this is defined? As for your notational question: after identification $\mathbb{Q}\Lambda_1\simeq \mathbb{Q}\Lambda_2,$ you can mod out this group by the sublattice $\Lambda_1+\Lambda_2$ that contains $\Lambda_1$ and $\Lambda_2.$ The requirement is that compositions of $\phi_1$ and $\phi_2$ with the projection become equal. | |
| Aug 10, 2010 at 16:56 | history | edited | mebassett | CC BY-SA 2.5 |
new title, tags.
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| Aug 10, 2010 at 16:42 | history | asked | mebassett | CC BY-SA 2.5 |