Timeline for Wanted: Quadratic Space in Characteristic 2 as a Counterexample to a Theorem of Arf
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2010 at 1:51 | history | edited | KConrad | CC BY-SA 2.5 |
added 353 characters in body; added 68 characters in body; added 12 characters in body
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| Jun 8, 2010 at 20:44 | vote | accept | KConrad | ||
| Jun 2, 2010 at 0:23 | answer | added | Skip | timeline score: 17 | |
| Apr 18, 2010 at 15:38 | comment | added | BCnrd | By pp. 104--108 in Albert's "Structure of Algebras", 2-torsion elts in Brauer group of any field of char. 2 are product of classes of quat. algs. (True in other chars by Merkurjev.) Thus, (1) says precisely "period = index" for ${\rm{Br}}(K)[2]$, a nicer formulation. Also, (2) says precisely that $Q$ is a non-degenerate quadratic form in $2n$ variables over $K$ with $n > 2$ such that ${\rm{SO}}(Q)$ is $K$-anisotropic (i.e., no $\mathbf{G}_ m$ as a $K$-subgroup). So sounds like a job for Galois cohomology of ss groups over general fields (like $K$); ask Parimala or Garibaldi at Emory. | |
| Apr 18, 2010 at 4:19 | history | asked | KConrad | CC BY-SA 2.5 |