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Results tagged with brauer-groups
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user 17907
Questions concerning Brauer groups of fields, rings, varieties, schemes or more general ringed spaces, invariants associated to Brauer classes such as index and period.
8
votes
Brauer group of projective space
Let $X$ be an $n$-dimensional projective space over a field $k$. Let $k_s$ be a separable closure of $k$, and $X_s$ the base change of $X$ to $k_s$. The algebraic part $\textrm{Br}_1(X)$ of the Brauer …
- 4,746
12
votes
Accepted
Brauer groups and field extensions
No: the conic $C:X^2+Y^2+1=0$ splits over the field $L=\mathbb{Q}(x)[y]/(x^2+y^2+1)$, since $(X,Y)=(x,y)$ is an $L$-point of $C$. However $L$ has no subfields algebraic over $\mathbb{Q}$ other than $\ …
- 4,746