Timeline for Brauer group elements of order $2$
Current License: CC BY-SA 3.0
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| Oct 24, 2012 at 12:58 | comment | added | Danny | And to expand on this, if $F$ is any field of characteristic not 2, and one considers the purely transcendental extension $F(x, y, z, w)$, then over this field, the product of the two quaternion algebras: $(x,y) \otimes__{F(x,y,z,w)} (z,w)$ is a division algebra, by Albert's criteria above, and hence has index 4. It has period two because each quaternion algebra does. | |
| Oct 24, 2012 at 2:38 | history | answered | Ray Hoobler | CC BY-SA 3.0 |