论文标题
四季节
Birational geometry of quaternions
论文作者
论文摘要
Quaternion代数$ b $的Hilbert类字段是一个代数$ \ Mathscr {h}（b）$，因此每一个双面理想的$ b $的每个双向理想都是$ \ m athscr {h}（b）$中的主要内容。我们研究了$ b $和$ \ mathscr {h}（b）$的化身，即附加到Quaternion代数的代数表面。事实证明，$ \ mathscr {h}（b）$的头像是通过bifational Map从$ b $的头像获得的。我们将此结果应用于函数字段类比。
The Hilbert class field of the quaternion algebra $B$ is an algebra $\mathscr{H}(B)$ such that every two-sided ideal of $B$ is principal in $\mathscr{H}(B)$. We study the avatars of $B$ and $\mathscr{H}(B)$, i.e. algebraic surfaces attached to the quaternion algebras. It is proved that the avatar of $\mathscr{H}(B)$ is obtained from the avatar of $B$ by a birational map. We apply this result to the function field analogy.
