Timeline for Higher Composition laws
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2011 at 18:30 | comment | added | GH from MO | @Franz: Let's look at (15) and the subsequent lines in Bhargava's paper. Multiplying each $I_i$ by $\kappa_i\in K$ has the effect of replacing each $a_{ijk}=\pi(\alpha_i\beta_j\gamma_k)$ by $a_{ijk}'=\pi(\kappa\alpha_i\beta_j\gamma_k)$, where $\kappa=\kappa_1\kappa_2\kappa_3\in K$ is of norm $1$. Why are the cubes $(a_{ijk})$ and $(a_{ijk}')$ equivalent? This must be a straightforward calculation that I am lazy to make (I am busy with other things). | |
| Dec 18, 2011 at 17:15 | comment | added | Franz Lemmermeyer | Of course the cube changes, but its equivalence class under the action of SL_2(Z)^3 does not. wstein.org/129/projects/schoenebeck/Composition.pdf | |
| Dec 18, 2011 at 16:45 | comment | added | GH from MO | Have you asked the author? | |
| Dec 17, 2011 at 19:03 | comment | added | Sina | By this definition the cube associated to a triple is not well defined because if we consider an equivalent triple then the cube will change. | |
| Dec 17, 2011 at 18:43 | comment | added | Franz Lemmermeyer | According to the definition, the product of these ideals must be contained in the domain (which is not assumed to be Dedekind in order to be able to work with orders in quadratic fields), and the product of their norms must be equal to 1. Where do you think Bhargava's proof goes wrong? | |
| Dec 17, 2011 at 18:19 | comment | added | Sina | In fact if we accept the definition then the proof of theorem 11 will have a serious mistake. | |
| Dec 17, 2011 at 18:16 | comment | added | Sina | I could not find any good source. Except a note from you which is not contained the main theorem of Bhargava paper. I mean Theorem 11 of the first paper. Could you please tell me some other notes? | |
| Dec 17, 2011 at 18:06 | comment | added | Franz Lemmermeyer | This is impossible without knowing your background and the points you are having trouble with. Googling for Bhargava and composition yields lots of sources containing very detailed descriptions. | |
| Dec 17, 2011 at 17:53 | history | edited | Sina | CC BY-SA 3.0 |
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| Dec 17, 2011 at 17:46 | history | asked | Sina | CC BY-SA 3.0 |