Timeline for Binary Quadratic Forms in Characteristic 2
Current License: CC BY-SA 2.5
3 events
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| Mar 18, 2010 at 20:53 | comment | added | BCnrd | Please read the last paragraph of my answer for my suggestion on the char-free approach to these matters for $n=2$. The point of the preceding part was to explain conceptually why discriminants should not play a role (apart from their non-vanishing) in the theory over suitable domains in char 2 for even $n \ge 2$. It may be a matter of taste, but I find the intervention of ${\rm{H}}^1(K, \mathbf{Z}/2\mathbf{Z})$ via the component group of ${\rm{O}}_ n$ in every characteristic (with $n$ even if in char. 2), and likewise over rings with trivial Picard group, to be incredibly illuminating. | |
| Mar 18, 2010 at 19:37 | comment | added | KConrad | This addresses issues over fields, while he is asking for an analogue to the integral theory. The only reason square discriminants look weird in the classical case is because those kinds of discriminants don't show up when you take discriminants of orders in quadratic number fields. I don't see a reason to be concerned over discriminants being perfect squares in characteristic 2. Once write something down in characteristic 2, then you may see if there some set of forbidden discriminants. Probably something connected to the Dickson invariant, in some integral sense, will appear. | |
| Mar 18, 2010 at 16:53 | history | answered | BCnrd | CC BY-SA 2.5 |