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Vanishing of the Brauer Group of a del Pezzo surface of degree 4
Journal of Number Theory ( IF 0.6 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.jnt.2020.03.008
Manar Riman

We explicitly construct a del Pezzo surface $X$ of degree 4 over a field $k$ such that $\operatorname{H}^1(k,\operatorname{Pic}\overline X)$ is isomorphic to $\mathbb{ZZ}/2\mathbb{Z}$ while $\operatorname{Br} X/\operatorname{Br} k$ is trivial. This proves that the algorithm to compute the Brauer group in [VAV] cannot be generalized in some cases.

中文翻译:

4 阶 del Pezzo 曲面的 Brauer 群的消失

我们在域 $k$ 上显式地构造了一个 4 阶的 del Pezzo 曲面 $X$,使得 $\operatorname{H}^1(k,\operatorname{Pic}\overline X)$ 同构于 $\mathbb{ZZ }/2\mathbb{Z}$ 而 $\operatorname{Br} X/\operatorname{Br} k$ 是微不足道的。这证明计算[VAV]中的Brauer群的算法在某些情况下不能推广。
更新日期:2020-09-01
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