论文标题
在理性数字领域的透明表面的异态自动形态群体
Birational automorphism groups of Severi-Brauer surfaces over the field of rational numbers
论文作者
论文摘要
我们证明，非平凡的versei-severi-brauer表面是〜$ \ mathbb {z}/3 \ mathbb {z} $和$（\ MathBB {\ althbb {z}/3 \ m athbb}， $（\ Mathbb {z}/3 \ Mathbb {z}）^2 $包含在$ \ Mathrm {bir}（v）$中，对于任何severi-- brauer surface $ v $，在$ 2 $和$ 2 $和$ 3 $和$ 3 $和$ 3 $和$（\ nathbb {z}/3 \ mathbb {z z}的特征领域上， $ \ mathrm {bir}（v）$对于任何severi-brauer surface〜 $ v $在一个特征领域，不同于$ 2 $和$ 3 $，其中包含一个非平凡的立方体统一根。
We prove that the only non-trivial finite subgroups of birational automorphism group of non-trivial Severi--Brauer surfaces over the field of rational numbers are~$\mathbb{Z}/3\mathbb{Z}$ and $(\mathbb{Z}/3\mathbb{Z})^2.$ Moreover, we show that $(\mathbb{Z}/3\mathbb{Z})^2$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface $V$ over a field of characteristic different from $2$ and $3$, and $(\mathbb{Z}/3\mathbb{Z})^3$ is contained in $\mathrm{Bir}(V)$ for any Severi--Brauer surface~$V$ over a field of characteristic different from $2$ and $3$ which contains a non-trivial cube root of unity.
